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https://m.scirp.org/papers/65205
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math
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Received 9 December 2015; accepted 27 March 2016; published 30 March 2016
The structural engineering is an open space where a great number of different needs converge in order to obtain a one solution. The high performance is often obtained using traditional structural typologies but increasing the element sections dimensions. Often the solution is to use different systems and typologies. Cables structures for example are particularly adapted to design large span but they need particular structures and shapes. This structural typology isn’t presented in the technical codes and also a preliminary design is impossible without a specific study. The particular shape isn’t presented in the wind action section of the codes and so is impossible to evaluate the wind action also for sample structures that use this system. Wind tunnel tests should be carried out. The wind tunnel experiments are often performed for a specific building and are used to study the wind-structure interaction in order to the design the building structures. However, in many cases the wind tunnel is a very important instrument of research. It’s important sometimes to study preliminarily a phenomenon in order to have a parametrization of the aerodynamic behavior. In both cases many numerical subroutines are programmed by the researchers to prepare the wind tunnel setup and to evaluate the wind tunnel experiments. Often, these numerical procedures are left detached and are created for the specific case studied. If the purpose of the research is a parametrization of a phenomenon it’s interesting to program codes generalizable in order to extend the research with a great number of different cases. Purpose of this paper is to describe a complete process of pre- and post- procession of wind tunnel data acquired with experiments to look for a parametrization of the aerodynamic behavior of a specific geometry: in this case the hyperbolic paraboloid geometry was studied. The objective is double: at first to give an example to follow in order to start a parametric experimental campaign, at second to give the possibility to extend the research. To obtain these results, the four different numerical procedures programmed will be described and the basic theory following will be summarized. In Section 2, the first numerical procedure to look for a sufficient representative geometric sample is presented. In Section 3, a numerical procedure programmed to obtain FEM three-dimensional models is proposed. In Section 4, the procedure to evaluate the wind tunnel acquisitions is summarized and in particular in Section 4.2.3, the application of the wind tunnel data to perform FEM analysis is described. Finally in Section 5, a research nonlinear structural analysis program is described to close the pre- and post-processing methodology. The results are a general main procedure to use for each similar research and also that can be used to extend this particular research with other geometries. The educational purposes of the paper want to sustain the research based on a personal idea.
2. Numerical Procedure for Preliminary Design Cables Net
The example of pre and post procedure to perform wind tunnel data consists in a research focused on the hyperbolic paraboloid geometry. The purpose of this research conducted by the Department of engineering and geology of Pescara (Italy) University and by the CRIACIV (Interuniversity Centre for Building Aerodynamics and Wind Engineering) wind tunnel laboratory, is to obtain a parametrization of the aerodynamic behavior of the hyperbolic paraboloid roofs (Rizzo F., et al., 2011; Rizzo F., et al., 2012; Rizzo F., 2012; Rizzo F., Sepe V., 2015). This particular shape is used to build tensile structures to cover for example sports arena, meeting or conference rooms. In the international codes there aren’t information about wind loads and in particular aren’t pressure coefficients to use as reference (ASCE 2005; AS/NZS 2002; CNR-DT 207/2008; CEN 2005). The difficulty to start a similar research is the little information this kind of structures; the wind tunnel tests are often performed for specific cases and are not generalizable; the first phase of the work is focused to look for a geometric sample to test in wind tunnel. The ratio between geometry and structural performances is very important for this kind of structures. The Hyperbolic paraboloid surface is characterized by four geometrical parameters: the sags and the spans of the two orders of parabola generating. In order to study the ratio between these four geometrical parameters and the structural response a numerical procedure is necessary - .
2.1. Main Program
Hyperbolic paraboloid cables net have a double curvature with different cable lengths and curvatures, and generally, different cable areas and pre-stresses. In addition, the shape plays a decisive role in the cables net deformation behavior under the action of external loads. In the cables net with opposite curvature, the two orders of cables become load-bearing or stabilizers depending on the direction of the acting load; the load-bearing cable is concave in the direction of the acting load. Therefore, in conditions of snow or wind suction, the two orders of cables reverse their curvature. This inversion is dangerous because it may lead to the instability of either the cables net or the border structures. The function adopted to describe the hyperbolic paraboloid is expressed by Equation (1), where x, y and z are respectively the spatial variables; x0, y0 and z0 are the coordinates of the origin of the axes a, b and c are the geometric coefficients of the function. The c parameter was set equal to 1, making all the parabolas that lying on the surface, parallel and of identical curvature.
It’s important to precise that the initial geometry is only an initial condition and that the real geometry of the net is defined on bases of the cables pre-stress. The loads effect modifies again the geometry and the objective of a correct design is to minimize the geometry initial variation with and without the pre-stress and the loads. The numerical procedure programmed starts from a fixed geometrical configuration and evaluates the final geometrical configurations with the pre-stress or with the other loads considered. The pre-sizing procedure implemented has the aim of obtaining pre-stress values and initial cables areas which permit an optimal structural response with a final geometry similar to the fixed geometry. A small difference between the fixed geometry and the deformed shape is important because the pressure coefficients evaluated in wind tunnel are valid for each load cases.
Geometries that allow an optimal configuration and a good relationship between shape and structural performance are identified investigating a set of about thousand different geometric configurations and extrapolating those which, for the same geometry, provide the best structural performance in terms of cable area and cables stresses, and therefore, in terms of structural weight and lower displacements in operating conditions.
In order to create a numerical procedure, the real three-dimensional case was simplified with a two-dimensional model called “Rope beam”, like illustrated in Figure 1. The two-dimensional structural model at the base of the
Figure 1. Rope beam, 2D structural system.
proposed procedure consists of two cables with opposite curvature which have a node at midspan in common. The equilibrium of the system forces in the node in common ensures the forces transmission between the two cables.
The prefixed assumptions are: vertical links, in tension or in compression, are treated as a continuous membrane between the two main cables; the horizontal displacements are neglected compared to the vertical ones; pretension is considered as an equivalent distributed load; the system congruence is required only in the central span node; the mutual actions between cables are uniformly distributed as the external load, and consequently, load-bearing and stabilizing cable have a parabolic configuration also in elastic regime.
The stiffness coefficients are considered, respectively for the load-bearing cable (C1) and stabilizing one (C2) defined as expressed in Equation (2) and Equation (3), where k1 and k2 represent, respectively, the stiffness of the load-bearing cable C1 and the stiffness of the stabilizing cable C2, defined in Equation (4); A1 and A2, f1 and f2, L1 and L2 are, respectively, area, sag and span length of the cable C1 and C2.
According to the iterative numerical procedure, given a fixed geometry, the external loads, the maximum stress limits and, finally, the maximum value of the forces to be transmitted to the support structures in conditions of maximum load applied, it is possible to compute the optimal cables area.
Cables areas are considered optimal if the cables stresses, under the maximum load design, respectively of compression and aspiration, are close to the upper and lower limit fixed in the hypothesis (σmax = 1700.0 MPa and σmin = 20.0 MPa). The global flow chart of the numerical procedure for cables net preliminary design is shown in Figure 2. It consist of two sub-procedures, respectively the procedure 1, illustrated in Figure 3, which allows to determine the optimum area of cable C1, and the procedure 2, illustrated in Figure 4, which allows to compute the area of cable C2 and therefore, the balance of the applied loads, depending on the area of cable C1.
Figure 2. Numerical procedure for cables net preliminary design, global flow chart.
Figure 3. Numerical procedure to preliminary design load bearing cables of a cables net.
Figure 4. Numerical procedure to preliminary design stabilizing cables of a cables net.
With reference to Figure 1, the prefixed geometric quantities are the cable sags (f1 and f2) and the span length (L1 and L2). Subscripts 1 and 2 indicate, respectively, load-bearing cables and stabilizing one. The considered load configurations are: initial equilibrium (“0”), in which acts only the cables net self-weight and in which the internal cables tensions are induced from initial pre-stress; application of permanent loads (“1”), in which, in addition to the cables net self-weight, acts membranes and/or roof panels’ weight; application of maximum snow action (“2”); application of maximum wind suction (“3”). The model predicted behavior provides that cable C1 reaches the maximum value of internal tension under the snow action, while cable C2 reaches the minimum value of tension; the cables length is modified under the load action, the initial geometry is bigger of lower in base of the direction of the load action. If the direction is gravitational the load bearing cables length increase, at contrary for the stabilizing cables. In this case, if wrongly designed, it is possible that the stabilizing cables curvature becomes inverse and the structure becomes instable. In Equations (1) and (2) the global cables stiffness and of the net is defined for the two order of cables; in Equations (4) and (5) and the single cables stiffness is defined depending on the cable area, sag, span, and finally on the cable material (E is the Young Module of the cable steel assumed equal to 165,000 Mpa).
The initial conditions are represented by the initial geometry, the load action considered and the material chosen in order to evaluate an initial value of cables stiffness, also a preliminary value of cables area (A0,1, A0,2) and strain (,) are fixed. This value will be iteratively modified. In Figure 3 the procedure 1 flow chart illustrates the first step of calculus. In the following the maximum snow action strain values are named, and the maximum wind suction strain values are named,. The suffix “i” used in the following equations indicates the generic load condition, is dead load, is permanent load, S is the maximum
snow action, W is the maximum wind suction. Like a start point the ratio between the cables stiffness is assumed equal to defined in Equation (6).
The initial geometrical cables length and is evaluated using the approximated formulation reported in Equations (7) and (8), depending on cables initial sag and span.
The initial cables internal traction and is evaluated as reported in Equations (9) and (10) assumed as the first forces of the mechanical problem; the initial horizontal traction equal to applied on the boundary structures is defined in Equation (11).
The initial balance between dead load and initial fixed is assumed as first condition. The load action is applied as an uniform distribution load (named equivalent load and in the following indicated as P) on the load bearing cable. In this particular case is assumed as a hypothesis that snow action is bigger than the wind suction. The reason is that there are snow loads value in the code for each altitude but there aren’t wind loads data for Hyperbolic paraboloid shape; so the flat roof pressure coefficients is chosen as a start point. The wind load value evaluated with the flat roof pressure coefficients is general lower than the snow action for an altitude major than 200 m, using the Eurocode. In order to preliminary design the cable net for the bigger load condition at first the snow action (S) is evaluated (load condition 2). Using the procedure 1 illustrated in Figure 3, the geometry variation of the load bearing cable (in this case C1) is evaluated in order to obtain the H2,1 defined by Equation (12). It’s important to note that and are the deformed sag and the cable C1 traction with the snow action.
In Equation (12), according to the Hook law is equal to, and and A are the strain and the cable area that satisfy the balance in load condition 2. Replacing in Equations (2), (3), (13), (14) are defined.
The load configuration, (load configuration 2, cable 1) that corresponds to snow action, is evaluated according to the Equation (15) obtaining by the Equations (10) and (12) and dimensionless respect the cable area A1. It is possible to define also according to Equation (16).
(iteration to) (15)
The relation that connect the “2” load condition and the “0” load condition is reported in Equations (17) and (18). The load balance reported in Equation (18) is obtained with an iteration of.
With the same procedure is fixed updating the value of. In conclusion, fixed an initial condition of traction the cables areas are defined according to the initial geometry wanted. In Figures 2-4 the flow charts of the procedure described are shown in order to summarize step by step the numerical proceedings. To validate the numerical procedure a comparison of the cables structural response with a Finite element method analyses (in the following FE) is done; in Figure 5(a) and Figure 5(b) the vertical displacements of the middle node is plotted for different cables areas but with same load applied (in this case equal to 2.2 kN/m gravitational and uniform load on the load bearing cable). The load bearing cable sag and span are equal to 4.44 and 80 m, the
stabilizing cables sag and span are equal to 8.89 and 80 m; in this case the ratio is assumed equal to 2. The
mean value of the percentage error is equal to 12%. This value appear acceptable if the approximation is considered. In the following the numerical procedure described in this section will be named NPPD (Numerical Procedure of Preliminary Design) (Elashkar I., Novak M., 1983; Lewis W. J., 2004; Majowiecki M., 2004) - .
2.2. The Analyzed Geometric Sample
In order to estimate a set of optimal geometry with the minimum cables areas and displacements (for equal forces transmitted to the support structure) - , a geometric parameterization taking into account the following parameters was carried out (Figure 6):
・ γ, the relationship between the cable sags, (f2/f1); 8 different values of γ, respectively equal to 0.43, 0:50, 0.70, 1.00, 1.50 1.80, 2.00, 2.33 were taken into account;
・ ρ, the relationship between the roof height and the maximum span length (H/Lmax); 6 different values of ρ, respectively equal to 1/3, 1/4, 1/5, 1/6, 1/8, 1/10 were taken into consideration.
・ α, the relationship between the span length (L1/L2); 4 different values of α, respectively equal to 1.50 (rectangular plan shape), 1.00 (square plan shape), 0.50 (rectangular plan shape), and variable, for structures with a circular plan shape were taken into account.
With the previously numerical procedure, 1008 different geometrical combinations were analyzed; only some configurations meet the optimization criteria pre-fixed in the hypotheses; in particular:
・ Cables net with L1 < L2 show better performance with lower values of forces transmitted to the supports.
・ Cables net with γ > 1 gives higher displacements but lower cables areas and therefore a lower structural weight.
・ “Optimal” values of γ, both as regards stress and structural weight optimization, are in the range between 1.5 and 2.5.
・ Low values of ρ give higher cables areas and therefore a higher structural weight; however, they gives “optimal” stresses with respect to cables net with high value of ρ.
・ The ratio between the obtained displacements with lower span lengths and those obtained with higher spans are lower compared to a direct proportionality.
Totally one thousand geometries are investigate in order to compare the structural response and to choose an optimal sample to test in wind tunnel. On the basis of these preliminary results, a representative geometric sample to be tested in the wind tunnel was chosen; in Table 1 the geometrical sizes of the full scale cable nets are listed for each plan shape. This phase of the work has produced a preliminary design numerical procedure with which it is possible to identify the sample to test in wind tunnel. A model scale equal to 1:100 is chosen to construct the models.
3. Numerical Procedure to Generate Cables Net Fe Models
Before wind tunnel test, tridimensional FE analyses are performed in order to simulate examples of full scale structures. The weight of the cables nets and their structural response under the snow action are studied to verify that the geometries chosen give a high structural response. In order to provide the geometric input for FEM models
Figure 5. (a) Comparison between FEM analysis and procedure of preliminary design and (b) percentage error.
Figure 6. Geometrical configurations investigated with the numerical procedure for cables net preliminary design.
with Hyperbolic Paraboloid shapes a numerical procedure has been implemented. At first, a step-by-step procedure allows to describe the two-dimensional domain and the three-dimensional domain firstly by choosing a reference system (Cartesian or polar). It is possible to compute the two-dimensional domain in two different ways; in both cases, the procedure allows to choose among four different conventional shapes: circle, ellipsis, rectangle and polygon. In the first case, the user must enter the geometric parameters of the shapes, for example, the radius or the side’s length. The second case allows calculating the curve function by choosing through an equations system obtained by setting some points coordinates on the domain. An additional option allows to directly
Table 1. Geometrical sample.
importing a.dxf (Drawing Interchange Format) file that describes the two-dimensional domain or, in the case of complex and irregular domains, it is possible to directly import the coordinates of the shape vertices. After setting the two-dimensional domain, the three-dimensional one can be set by choosing among seven prefixed shapes (sphere, ellipsoid, flat, hyperbolic paraboloid, elliptic paraboloid, a one slope hyperboloid and a two slopes hyperboloid). Also in this case it is possible to directly insert geometric parameters and surfaces coefficients, or compute their functions through an equations system obtained by setting some points coordinates on the surface. The next step concern the insertion of the cables spacing in the two directions, X and Y in the case of Cartesian coordinates, or meridians and parallels in the case of polar coordinates. In the case of Cartesian system, the procedure computes the equation of each line that describes the cable, and then intersects lines with the 2D domain generating a set of nodes and computing the respective coordinates on the plane, pi(xp, yp). In the next step the procedure projects the evaluated nodes on the spatial surface, identifying the third coordinate zp.
In the exporting phase, 3 different files can be saved: a.txt (text file) for input that contains the number of nodes and their coordinates; a.dxf with the cables net vector model; and a file that contains the functions equations of the created curves and surfaces. Thanks to this procedure, FEM model for nonlinear dynamic analyses can easily be generated. Figure 7(a) shows the intersection between the 2D domain and the 3D domain, while Figure 7(b) shows the simplified flow chart of the numerical procedure. Finally, in Figure 7(c) an example of hyperbolic paraboloid mesh with square plan shape generated is reported. Static and modal FE analyses are performed using the numerical models tested. Using the .dxf files generated the wind tunnel models are constructed made of wood. In the following the numerical procedure described in this section will be named Numerical Procedure to Generate Finite Element Models, in the following NPGFM - .
4. Wind Tunnel Test
The wind tunnel is a tool used in aerodynamic, aeroelastic and fluid mechanics research to study the effects of
Figure 7. (a) Intersection between 2D and 3D domain; (b) Tensile mesh generator flow chart; (c) Hyperbolic paraboloid mesh with square plan shape.
air moving past solid objects rigid and flexible. A wind tunnel consists of a tubular passage with a particular geometry where the object to test is in the middle of the test chamber. Air is made to move past the object by a powerful fan system or other means. The wind tunnel model is instrumented with suitable sensors to measure aerodynamic forces, pressure distribution, or other aerodynamic-related characteristics. In this experience the models are rigid and the goals were to acquire pressure coefficients - .
The CRIACIV (Inter-University Research Center for Building Aerodynamics and Wind Engineering) wind tunnel located in Prato (Italy) is used to perform aerodynamic experiments. A layout of the wind tunnel is illustrated in Figure 8. The choice of the turbulence intensity and so of the wind tunnel speed profile is important, too. For this research a more general possible condition was necessary. A medium urban profile is chosen for the boundary layer. In Figure 9(a) and Figure 9(b) the boundary layer development artificial roughness (wood panels) (a), spires (b) are shown and in Figure 9(c) and Figure 9(d) the speed and turbulence profile is reported. The mean value of the wind tunnel speed at the roof level is between 16 and 20 m/s, the turbulence at the same level is between 12% and 15% (Simiu E., Scanlan, R. H., 1986).
The test models are made in wood and their geometrical scale is fixed equal to 1:100; the reason of this choice is to have big models and so easy to construct but with a not much high blockage coefficients. The constructions follows the geometry designed using the numerical procedure described in Section 3. Test models pictures are shown in Figure 10, respectively with a square plan (a), rectangular plan (b), circular plan (c) and elliptical plan (d). The geometry of the wind tunnel models is described in Table 1. Each model was instrumented (Figure 11(a) and Figure 11(b)) varying from 175 to 211 pressure taps distributed on the roof like shown in Figure 11(c). Each pressure tap was connected to a pressure transducers with a pneumatic connection made of Teflon tubes with 1.3 mm internal diameters (Figure 11(a) and Figure 11(b)). Data for 16 different wind angles were acquired at a frequency of 252 Hz and for 30 seconds obtaining, for each pressure tap, a pressure time history of 7504 values.
The ratio between the models size and the test chamber section size is very important (φ). If this ratio is big (2% or 3%) the blockage effects increases pressure coefficients and correction factors are necessary. In this case the blockage effect is not negligible and so a blocking coefficient β was considered. According to Equation (19) φ is evaluated and the correction factor β is estimate. Atot is the wind tunnel test section area and Alateral is the model section area.
In Table 2 blockage values and the correction coefficients for each tested model are reported. They are in a range between 1.5% and 7.7% with peaks for geometries p.2, p.4, p.6, p.8, p.15 and p.17 (highest model). The correction values for the pressure coefficients vary from a minimum of 2% to a maximum of 4%.
Figure 8. CRIACIV wind tunnel image (a), elements (b): (A) entrance; (B) boundary layer development zone; (C) test chamber (section size 2.40 × 1.60 m); (D) connection zone; (E) engine (160 kW); (F) diffusion T-shape.
Figure 9. Boundary layer development artificial roughness (wood panels) (a), spires (b); (c) velocity and (d) turbulence profiles.
Figure 10. Hyperbolic parabolic roofs: (a) square plane; (b) rectangular plane; (c) circular plane; (d) ellipltical plane .
Figure 11. Wind tunnel acquisition data, (a) and (b) model instrumentation, (c) example of pressure taps distribution.
Table 2. Blockage values.
4.2. Data Processing
Experimental data consist in pressure expressed in mmH2O deriving by the transducers acquisition; a numerical procedure is needed in order to obtain a double goal: at first pressure in Pascal and pressure coefficients located on the roof and at second, forces time history to use in FEM analysis. For this reason a numerical procedure have to transform data into pressures, then evaluate the pressure coefficients, then estimate the maximum, minimum and mean values of these coefficients, and finally transform the pressure coefficients into forces to be applied on the FEM model. The first phase concerns the graphic aspect, with the preparation of the geometry of the pressure coefficients map; the second stage involves the implementation of the subroutine for the evaluation of the pressure coefficients and the third phase provides the forces calculation.
4.2.1. Pressure Coefficients Maps
In order to obtain pressure coefficients maps to describe the pressure distribution on the roof and sides of the model, the surface was discretized in polygons surrounding each pressure taps. The Thiessen (Voronoi) polygons theory is adopted. It consists to define individual areas of influence around each of a set of points. Thiessen polygons are polygons whose boundaries define the area that is closest to each point relative to all other points.
They are mathematically defined by the perpendicular bisectors of the lines between all points. The process goes through several steps: collects the points from a point layer (vertices if the source is a polyline or polygon layer), clean duplicate points, generates Convex Hull, creates a TIN structure, generates perpendicular bisectors for each tin edge, builds the Thiessen polygons and, finally, clips the Thiessen polygons feature class with the convex hull. A specific numerical procedure is programmed for this section. An example of Thiessen polygons distribution is illustrated in Figure 12. It is possible to note that if the pressure taps distribution is not geometrically regular with a structured grid, the shape of the Thiessen polygon is irregular. For each polygon one value of pressure coefficient is associated - .
4.2.2. Evaluation of Pressure Coefficients
During wind tunnel tests the model is fixed in the test chamber, in Figure 13(a) a picture of a model during the test is shown. The tubes connected to the transduces sent an input to the computer that measure the pressure variation in mm H2O. The experimental data needs to be transformed in pressure coefficients. Pressure coefficients (Cp), is a dimensionless number which describes the relative pressures throughout a flow field in fluid
Figure 12. An example of Thiessen polygons distribution.
Figure 13. (a) Model in the wind tunnel; (b) Pressure coefficients map (mean values); (c) Pressure coefficients 3D mesh; (d) Typical forces time history.
dynamics; it is evaluated by the ratio between the difference of the local pressure and the undisturbed flow pressure, and undisturbed dynamic flow pressures are evaluated for each wind direction. Maximum (Cp,max), minimum (Cp,min) and mean values (Cp,m) of the pressure coefficients are extracted from the obtained pressure time histories. Subsequently, pressure coefficients maps were plotted. An example of Mean value of pressure coefficients map is shown in Figure 13(b). Minimum and maximum pressure coefficients have been calculated using a probabilistic method according to the Gumbel method (Gumbel, E.J., 1958) following the procedure proposed in (Cook N.J., Mayne J.R., 1979), (Cook N.J., Mayne J.R., 1980), associated with a probability of 22% that it will be exceeded, as is done by Eurocode 1. For each pressure taps and for each model, the numerical procedure computes a pressure coefficients time history of 7504 points, a pressure coefficients matrix consisting of 7504 rows and a number of columns equal to the number of pressure taps. Moreover, for each model the procedure calculates three vectors containing the mean, maximum and minimum value of the pressure coefficient. In the following the numerical procedure described in this section will be named NPWDP (Numerical Procedure for the Wind tunnel Data Process).
4.2.3. Data Exchange between Wind Tunnel and FEM Analysis
In order to use experimental data to perfume FEM analyses, the same surface discretization between wind tunnel test model and FE model is necessary. Often that is impossible because the number of pressure taps used for each models is generally less than the FE model nodes. Also in this case it was happened. The mean value of pressure taps number used on the roof is 90, the number of nodes used in FEM analysis to describe the cable net is about 1700. A numerical procedure to extend the experimental data on the FEM mesh is necessary. There are to more used possibilities: the first is obtained overlapping the FEM mesh and the Thiessen polygons distribution, the same pressure coefficient is used for all FEM nodes that are surrounding by polygon. A second way is to estimate a mathematical procedure to interpolate the experimental data respect the FEM mesh. Both procedures were implemented. The first solution follows the following sequence: the polygons edges coordinates (Cartesian reference system) are determined; a scan of the FEM nodes coordinates is been done in order to check the proximity from the polygon edge. The nodes that have coordinates between the polygon minimum and maximum coordinates are in the polygon. The second procedure is more difficult. The first phase is the same to the previous solution, but during the scan a value of pressure coefficients for each node is assumed; the values is evaluated using the inverse distance weight (IDW) interpolation method (Borrough P.A., 1986; Greville T.N.E., 1969; Hohn M.E. (editor), 1998). An example of 3-dimensional pressure coefficients map obtained using this last method is shown in Figure 13(c). Using the pressure coefficients time history assumed for each FEM nodes, a wind loads time history is evaluate. In this case in order to obtain the structural response of a cable net under wind action, a localization of the net is necessary. A value of wind kinetic pressure and geographical aspects are chosen. A preliminary ramp is added by the load history, it has a length equal to about 1% of the history length. In Figure 13(d) an example of the load history is shown for a cable net center point (N1) (Shen S., Yang Q. 1999). In the following the numerical procedure described in this section will be named NPED (Numerical Procedure to Exchange Data). In Figure 14 the procedure is summarized - .
5. Wind-Structure Interaction with Time History Analysis
In order to estimate cables nets structural response, Nonlinear Dynamic Analyses have to be performed. The analyses are conducted on the tested sample using numerical procedures implemented by Full Professor PieroD’Asdia staff; the procedures are merged in a main program in the following named TENSO. It isn’t a commercial software and it was born as a set of numerical procedures and subroutines merged step by step from 1980. The description of these procedures has never been published.
The Non Linear Structural Analysis Program
The structural analysis program (in the following TENSO) is designed for static and dynamic analysis with step-by-step integration of nonlinear geometric three-dimensional structures. It contains cable and beam finite elements and permits the study of wind-structure interaction with generation of wind histories and simulation of aeroelastic phenomena (Crisfield M.A., 1991). Nonlinear static analysis were carried out with the wind action evaluated for mean, minimum and maximum pressure coefficients while nonlinear dynamic analysis were performed by applying wind action as a forces time history computed with the previously described numerical procedure. With TENSO is possible to compute parabolic cables in two ways: in the first case, the cable can be divided in an appropriate number of elements that are rectilinear cable, in the second case elastic catenary configuration or parabolic cable can be used. The first case is applicable only with nodal loads. Possible applications of this methodology are suspension bridges with a distance between the hangers sufficiently small compared to the cable span length, and cables nets with a small spacing between cables compared to the maximum span length. For this kind of structures the global stiffness matrix is updated for each load step through the assembly of stiffness matrices of the elements varied according to the strain found in the previous step. In this way the software takes into account the geometric nonlinearity of the structure. As regards to the beam finite element, it is possible to choose among a beam with a uniform or a variable section. For each case it is possible to introduce prestressing actions or tractions as well as thermal loads. In particular, the beam finite element with variable section provides the calculation of ten coefficients in order to describe the area variation and the moment of
Figure 14. Flow chart of the wind tunnel data processing.
In TENSO, secant method is used as a check method that permits to stop the analysis with a unbalanced solution. Using the step by step incremental method, nonlinear problem can be transformed in a succession of linear problems. Each calculation step stores loads and strains history evaluated during the previous step. For each analysis step, a small enough part of load (ΔP) necessary to ensure that is possible to use the elasticity method is applied. However, this simple and classical approach presents the difficulty to evaluate the exact dimension of load step and so the exact step of analysis. A non-appropriate chosen range can cause an inexact solution. In order to solve it, TENSO uses the method with the variable stiffness matrix; this method is a vector version of the Newton-Raphson modified method about nonlinear equation systems. The Newton-Raphson procedure guarantees convergence if and only if the solution at any iteration is close to the exact solution. Therefore, even without a path-dependent nonlinearity, the incremental approach (i.e., for subsequent load steps) is sometimes required in order to obtain a solution corresponding to the final load level. If the displacements are large, the product between the stiffness matrix, evaluated on the basis of the solution of the previous step and on the basis of the stresses, and the displacements vector, give the internal force vector, not equilibrate with the external forces vector according to Equation (20), where is the stiffness matrix, is the displacements vector, is the external forces vector; the difference between these two forces vectors represents the imbalance force vector, according to Equation (21), where R is the residual vector and P is the internal forces vector. In the following step, this vector is applied as an external load modifying the displacement vector with a residual value of displacements, according to Equation (22) where is residuals values of displacements to update the geometry, and so updating the structure geometry.
In order to solve nonlinear dynamic analyses, TENSO uses the Newmark-beta method, a numerical integration method used to solve differential equations. It is used in finite element analysis to model dynamic systems. In order to illustrate the use of this family of numerical integration methods, the solution of a linear dynamic system have to be firstly considered. In 1962 Newmark’s method in matrix notation was formulated, stiffness and mass proportional damping was added, and the need for iteration by introducing the direct solution of equations at each time step was eliminated. The time dimension is represented by a set of discrete points each a time increment apart. The system is solved at each of these points in time using as data the solution at a previous time. The procedure follows these subsequent phases: reading of initial boundary conditions; assembly of the stiffness matrix, setting β and γ, Newmark method parameters that control the stability and the accuracy of the integration procedure. They are equal to 1/4 and 1/2 respectively; assembly of the vector forces; step by step calculation with iterative process and convergence check. For each integration step, a check of the solution precision is done in order to evaluate if it is necessary to modify the integration step dimension. Generally, a more precise solution needs a very small integration step and so a higher computational work. Unbalanced loads are evaluated according to the Newmark’s algorithm, as the difference between the reactions and the applied external loads. In TENSO, a correction of this algorithm is implemented: the precision of solution is evaluated as a ratio between unbalanced loads and applied external loads for each unconstrained degree of freedom. At each integration step, unbalanced loads are added to the next load step, in order to obtain an optimal solution (Melchers R.E., 1987; Smith I. M., Griffiths D.V., 1982). In Figure 15, a global flow chart of TENSO is summarized. The main pro-
Figure 15. Nonlinear structural analysis program global flow chart.
gram of the numerical procedures described in this section in the following will be named NPSA.
In order to demonstrate the validity of the procedure, two examples of different structures covered with cables net are described: the first one is a project proposal under review (2012) of a roller skates arena and the second is basketball arena; the last one is a project proposal for the renovation of an existent sports arena (2007).
6.1. Project of a Roller Skates Arena
The building designed is located in Pescara, middle Italy, and its purpose is to cover an existent open space used for roller skates competitions (Rizzo et al., 2014). The building has a circular plan and is covered with an Hyperbolic Paraboloid cables net roof. The most important geometrical parameters are summarized in Table 2. The horizontal traction (referring to Equation (11)) is absorbed by a series of external pillars and beams located around the building like are illustrated in Figure 17(c). In Figure 17(a) a global view of the urban contest and in Figure 17(b) a significant plan of the building are shown. The geometry chosen is one of the optimal geometries studied and described in Figure 16 and obtained by the procedure described in Section 2. In this phase of the project wind tunnel experiments results obtained with the parametric study described in Section 3 are sued. Of course after this first preliminary phase some specific wind tunnel experiments are necessary to study aerodynamic and aeroelastic effects. The pressure coefficients maps (Rizzo et al., 2011 and Rizzo, 2014) for two significant angles used to evaluate the wind action are shown in Figure 18. The wind direction of 0˚ are parallel to the stabilizing cables and at contrary, the wind direction of 90˚ are parallel to the load bearing cables.
A FEM model is analyzed and geometrical non-linear analyses are carried out in order to design the structural components of the building. The procedure described in Section 3 is followed to define the FEM models and some pictures are illustrated in Figure 19. The mechanical parameters are reported in Table 3, where D is the externa diameter of the building, A1 and A2 are respectively the load bearing cables and the stabilizing cables, ε1
Figure 16. Procedure for the evaluation of tensile structure behaviour.
Figure 17. External views of the roller skates arena
and ε2 are the strains cables for the load configuration number 1 (according to Section 2); Hb is the drum high of the building, H is equal to the f1 + f2.
Using the numerical procedure described in Section 4, nonlinear analyses are carried out in order to study at first the structure deformation and its natural frequencies. Modal analyses and then a dynamic time history analysis are permed using the wind tunnel experiments results. Some results are illustrated in Figure 20 and Figure 21. In particular the first 9 modes shape are reported in Figure 20 and are listed in Table 4, the deformation under 0 wind action is reported in Figure 21. Observing the cables area values reported in Table 3 and considering that 40 load bearing cables and 40 stabilizing cables are used, we note that the structural weight of the roof is really low, the cables net weight is only 1.5 × 10−2 kN to square meters. One aspect ore is important to note: the first 9 modes are totally roof’s mode and the periods are very high. This structures are particularly optimal in seismic zones because are flexible and ductile.
6.2. Project of a Basketball Arena
The project purpose is to substitute a truss structure used to cover a sport arena with a cable net structure. The advantages are many and the most important is the easy of maintenance. The great numbers of bolted nodes often require maintenance and the trusses require a very repetitive protective painting. The occasion to begin the
Figure 18. Pressure coefficients maps, (a) 0˚ and (b) 90˚.
Figure 19. FEM models views.
Table 3. Geometrical and mechanical parameters.
Figure 20. Modes shape deformation.
Table 4. Natural frequencies and periods.
Figure 21. Upward deformation under 0˚ wind action.
building renovation was the championship European basketball competition (2007) (Rizzo et al., 2012). The proposal is being evaluated by the municipality government for the future renovation.
The idea is to realize an external structure with a square plan in order to have a total open space into the arena. Some pictures of the actual structure and the future modification are illustrated in Figure 22. A square plane is chosen in order to respect the actual shape of the building and its urban contest. A series of stays are used to absorb the horizontal traction of the cables net, like is shown in Figure 22. In Table 5 the main geometrical parameters are listed and the cables areas and strains for the load configuration number 1 (according to Section 2).
The structural response is evaluated with Non-Linear analyses carried out with a FEM model modelled with the numerical procedure described in Section 3. Some pictures of the FEM model are shown in Figure 23. Using the numerical procedure described in Section 5 the Natural frequencies and displacements under loads combinations are evaluated, too. In Figure 24 the first 10 modes shape deformations are reported and in Table 6 their values are listed. It’s interesting to note that the period is higher than the other geometry described in Section 7.1; it’s caused by many reason, at first the plan geometry because the circular shape gives a more rigid border structure, at second the cables areas and strains are lower for this geometry, finally, this structure is also higher than the previous.
The wind action is applied on the FEM model like a series of time histories evaluated by wind tunnel experiments and a dynamic analysis is performed. In Figure 25 a view of the structure deformation under 90˚ wind action is shown; it is interesting to note that this direction is particularly critic for Hyperbolic paraboloid cables net because the suction is higher than the other angles (Rizzo et al., 2011), so it is particularly important that the suction not decreases too the load bearing cables strain. In this case, like is reported in Table 7, the ratio between load bearing cables strains with and without wind is equal to 0.85 (reduction equal to 15%). In Table 6 the structural response in term of cables strains, traction and deformation variation, is reported; T1 and T2 are the cables traction evaluated according to the Equation (10), Δf is the sag variation.
Every time that an experiment is processed, a great number of numerical procedures are programmed by researcher to control the process. These numerical procedures are often isolated and programmed again for every different case of study. An interesting goal is to create a free open domain where the numerical procedures evaluated are merged, added, modified by researchers with the aim to obtain a common space of use. With this purpose, the present paper described a methodology followed to prepare a wind tunnel test and to process results. Five different steps NPPD → NPGFM → NPWDP → NPED → NPSA give a one complete numerical procedure that can be expanded, modified or completed by everyone. In this specific case the subroutines can be modified to capture more and more different geometries or structural typologies with the aim to obtain a globalized virtual space of calculus. This paper is focused to wind tunnel tests because they are generally complex,
Figure 22. (a) External view of the actual structure; (b) Future modification of the building.
Table 5. Geometrical and mechanical parameters.
Figure 23. FEM model views.
Figure 24. Modes shape deformation.
Table 6. Natural frequencies and periods.
expansive and long test: a previous efficient and detailed preparation is necessary before and a great capacity to synthesize the results obtained is necessary after. With the methodology used the goal is obtained: in fact, at first the preliminary design procedure permits to choose the sample to test; at second the FEM generation procedure permits to obtain FE model for FEM analyses and a guide to construct wind tunnel test models; at third the
Figure 25. Upward deformation under 90˚ wind action.
Table 7. Structural response.
processing data procedure permits to evaluate the experimental data and to prepare the input of the FEM analyses. Finally, the nonlinear structural analyses procedure permits to evaluate the structural response. The global flow chart is illustrated in Figure 16.
Special thanks to Full Professor PieroD’Asdia for the research coordination, to Engineer Massimiliano Lazzari for his for his collaboration in the planning process described in Section 2, to Engineer Fabrizio Fattor for his collaboration in the planning process described in Section 3, to Associate Professor Gianni Bartoli and the CRIACIV Wind tunnel boundary layer staff, in particular Engineer PhD Tommaso Massai and Lorenzo Procino, for the coordination of the wind tunnel tests and the numerical procedure programming described in Section 4, to Architect PhD Federica Speziale for the FEM analysis described in Section 5, finally to PieroD’Asdia, FabrizioFattor, Salvatore Noè and Luca Caracoglia for the calculation program described in Section 5.
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https://www.arxiv-vanity.com/papers/1809.02749/
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Revisiting the asymptotic dynamics of General Relativity on AdS
The dual dynamics of Einstein gravity on AdS supplemented with boundary conditions of KdV-type is identified. It corresponds to a two-dimensional field theory at the boundary, described by a novel action principle whose field equations are given by two copies of the “potential modified KdV” equation. The asymptotic symmetries then transmute into the global Noether symmetries of the dual action, giving rise to an infinite set of commuting conserved charges, implying the integrability of the system. Noteworthy, the theory at the boundary is non-relativistic and possesses anisotropic scaling of Lifshitz type.
The dynamics of Einstein gravity in three spacetime dimensions is described by global degrees of freedom that can be identified only once a precise set of boundary conditions is provided. In the case of asymptotically AdS spacetimes equipped with Brown-Henneaux boundary conditions, the asymptotic symmetry group is generated by two copies of the Virasoro algebra Brown:1986nw . Demanding that the Lagrange multipliers –given by the lapse and shift functions in an ADM foliation– are held constant at infinity, the reduced phase space of the Einstein field equations is described by Virasoro modes that evolve according to
where is the AdS radius and are coordinates parametrizing the cylinder at infinity. The symmetry algebra and the form of the latter equation is consistent with the description in terms of the boundary theory; it is well–known that the asymptotic dynamics for these boundary conditions is described by left and right chiral bosons Coussaert:1995zp ; Henneaux:1999ib 111As shown in Coussaert:1995zp ; Henneaux:1999ib , it is possible to rewrite the action of two chiral bosons as a Liouville theory. This is accomplished by performing a Bäcklund transformation that excludes the zero mode sector of the chiral bosons.. The components of the stress–energy tensor of the chiral bosons are given by the Virasoro modes , so that equation (1) corresponds to its conservation law. Note that for the boundary conditions of Brown and Henneaux, the chiral bosons and their corresponding left/right energies fulfill the same equations.
Recently, a new family of boundary conditions connecting Einstein gravity on AdS with the Korteweg-de Vries (KdV) hierarchy of integrable systems has been proposed in Perez:2016vqo . The possible choices of boundary conditions are labeled by a nonnegative integer , corresponding to the -th representative of the hierarchy. The Brown-Henneaux boundary conditions are recovered for , so that the modes fulfill (1); while for , the modes are described by noninteracting movers, satisfying the KdV equation
where is the Newton constant. For the asymptotic symmetry algebra turns out to be spanned precisely by the infinite set of commuting charges of KdV.
One of the main purposes of our work, is to unveil the precise form of the action principle that describes the dynamics of the underlying fields of the dual theory at the boundary, from which the field equations of the KdV hierarchy emerge from a conservation law. In order to carry out this task, it is convenient to use the Chern-Simons formulation of three-dimensional gravity Achucarro:1987vz ; Witten:1988hc . We then perform a Hamiltonian reduction similar to the one of Coussaert, Henneaux and van Driel Coussaert:1995zp . A distinguishing feature of our derivation is that, as the boundary conditions for actually precludes one from passing through the standard Hamiltonian reduction of the Wess–Zumino–Witten (WZW) model Forgacs:1989ac ; Alekseev:1988ce , one has to circumvent this step through imposing the boundary conditions in the action principle from scratch. In this way, one obtains a novel action principle for the dual theory, whose field equations are described by two copies of the hierarchy of ‘‘potential modified KdV’’ (pmKdV) equations of opposite chirality222A list of the first four equations of the pmKdV hierarchy is given in appendix B..
The paper is organized as follows. In the next section, we revisit the boundary conditions of KdV-type in the context of 3D gravity with negative cosmological constant. In section 3, the dual theory at the boundary is obtained from the Hamiltonian reduction of the Chern-Simons action endowed with a suitable boundary term. The field equations are also analyzed. Section 4 is devoted to study the global symmetries symmetries of the dual action principle at the boundary. We conclude in with some comments in section 5.
2 General Relativity on AdS and the KdV hierarchy
and the Chern-Simons level is given by . Here, is the three-dimensional manifold with coordinates , where represents time, stands for the radial coordinate and is an angle. The generators of the algebra, given by , with , are chosen such that the commutators and the invariant non-degenerate bilinear form read
In order to describe the asymptotic form of the gauge fields, it is useful to make a gauge choice as in Coussaert:1995zp , so that the connection reads
where stand for the dynamical fields, and correspond to the Lagrange multipliers. In the asymptotic region, the field equations, , reduce to
where the operators are defined by
The asymptotic symmetries can then be explicitly found by demanding the preservation of the auxiliary connection under gauge transformations, , where is a Lie-algebra-valued parameter. Thus, the asymptotic form of is maintained for gauge transformations spanned by parameters of the form
where are arbitrary functions of and , provided that the dynamical fields transform as
Preserving the temporal component of the gauge field then implies the following condition for the variation of the Lagrange multipliers
It is worth stressing that the boundary conditions turn out to be fully determined only once the precise form of the Lagrange multipliers at the boundary is specified. The results of Brown and Henneaux Brown:1986nw are then recovered when the Lagrange multipliers are held constants at infinity . A simple generalization is obtained by choosing arbitrary functions of the coordinates, so that are kept fixed at the boundary Henneaux:2013dra ; Bunster:2014mua . Different choices of boundary conditions, in which the Lagrange multipliers are allowed to depend on the dynamical fields and their spatial derivatives, were proposed in Perez:2016vqo . Hereafter, we focus in a special family of boundary conditions of KdV-type, being labeled by a non negative integer . In this scenario, the Lagrange multipliers are chosen to be given by the -th Gelfand-Dikii polynomial Gelfand:1975rn evaluated on , i.e.,
The polynomials can be constructed by means of the following recursion relation333Note that the normalization of the Gelfand-Dikii polynomials used here differs from the one in Perez:2016vqo .
Thus, in the case of one obtains that , which reduces to the boundary conditions of Brown and Henneaux Brown:1986nw . In this case, equation (13) implies that the parameters are chiral, while the dynamical fields also do, since the field equations (9) reduce to (1). The next case corresponds to so that the choice of Lagrange multipliers is given by , and hence, the field equations in (9) reduce to KdV
In the remaining cases, , the field equations are then given by the ones of the -th representative of the KdV hierarchy.
Note that for , the Lagrange multipliers acquire a non-trivial variation at infinity. Nonetheless, as shown in Perez:2016vqo and further explained in the next section, the action principle can be well defined because each of the Gelfand-Dikii polynomials can be expressed in terms of the variation of a functional, i.e.,
where stand for the conserved quantities of KdV, and are the corresponding densities 444A list with the first Gelfand-Dikii polynomials, conserved quantities of KdV and the corresponding field equations of the KdV hierarchy is given in appendix A.. Furthermore, equation (13) becomes a consistency relation for the time derivative of the asymptotic symmetry parameters . Thus, for , assuming that the parameters depend exclusively on the dynamical fields and their spatial derivatives, but not explicitly on the coordinates, the general solution of the consistency relation is given by a linear combination of the form
with constants. This infinite set of symmetries then gives rise to conserved charges, which can be written as surface integrals by means of the Regge-Teitelboim approach Regge:1974zd . The variation of the conserved charges associated to the gauge transformation generated by a parameter of the form (11) that spans the asymptotic symmetries, is given by
The asymptotic symmetries are then canonically realized. A straightforward way to obtain the asymptotic symmetry algebra in terms of Poisson brackets is given by the relation
The cases and are then very different in this context. Indeed, for the algebra turns out to be abelian
while for , which corresponds to Brown-Henneaux, the algebra of the conserved charges is given by two copies of the Virasoro algebra with a non-vanishing central extension.
Some interesting remarks about the metric formulation are in order. It is worth highlighting that the reduced phase space for the boundary conditions of KdV-type, for an arbitrary non negative integer , always contain the BTZ black hole Banados:1992wn ; Banados:1992gq , which corresponds to the configuration with constants Perez:2016vqo . Indeed, the field equations of the KdV hierarchy are trivially solved in this case, and the spacetime metric in the ADM decomposition is such that the lapse and the shift correspond to a non-standard foliation, determined by . Specifically
Furthermore, the boundary conditions described by (7) and (8), with given by (14) are such that the fall-off of the metric somewhat resembles the one of Brown-Henneaux. Indeed, in a Fefferman-Graham-like gauge, the spatial components of the metric and its conjugate momenta behave as
However, the key difference arises in the asymptotic behavior of the lapse and shift functions, which read
Hence, for they are allowed to fluctuate at leading order, in sharp contrast with the fall-off for that corresponds to the Brown-Henneaux boundary conditions for which .
3 Dual theory at the boundary
In this section, we perform a Hamiltonian reduction of the action (3) by explicitly solving the constraints of the theory. The boundary conditions for the gauge field correspond to (7) and (8), where the “chemical potentials” in (14) are given by the -th Gelfand-Dikii polynomial . The reduction is carried out for a generic value of .
3.1 Hamiltonian reduction
The Hamiltonian reduction of Chern-Simons theory in the context of three-dimensional gravity has been discussed extensively in the literature, see e.g., Coussaert:1995zp ; Henneaux:1999ib ; Rooman:2000zi ; Barnich:2013yka . For the standard choices of boundary conditions Brown:1986nw ; Barnich:2006av , the classical dynamics can be obtained from the Hamiltonian reduction of the WZW theory at the boundary Witten:1988hf ; Elitzur:1989nr ; Forgacs:1989ac ; Alekseev:1988ce . Nonetheless, for the boundary conditions of KdV-type, the reduction does not lead to the usual WZW theory at the boundary, since for a generic value of the components of the gauge field at the boundary are no longer proportional, and hence, the Kac-Moody symmetry appears to be manifestly broken (except when which corresponds to Brown-Henneaux). Nevertheless, as explained below, the reduction can still be successfully performed because the boundary conditions can be appropriately implemented in the action principle.
The resulting reduced action at the boundary gives rise to a different hierarchy of integrable equations, labeled by the integer . The simplest case () corresponds to two chiral bosons of opposite chirality Coussaert:1995zp ; Henneaux:1999ib . For we obtain a novel action principle, whose field equations are given by two copies of the pmKdV equation (see e.g. olver2000applications ; wang2002list ). In the remaining cases () the action of the dual theory describes the other members of the pmKdV hierarchy. The integrability of this hierarchy is explicitly checked the next section.
We start with the action (3) written in explicit Hamiltonian form
where stand for appropriate boundary terms generically needed in order to have an action principle that is well defined. It is worth pointing out that the boundary can be located at an arbitrary fixed value of the radial coordinate. Here is the spatial part of the Levi-Civita symbol, while is the curvature . We choose , and dot stands for derivative with respect to . The action (29) attains an extremum when the field equations hold, provided that
Note that for the Brown-Henneaux boundary conditions (), the components of the gauge field satisfy at the boundary, and hence, can be readily integrated. However, for the boundary conditions of KdV-type, with the temporal and angular components of the gauge field at the boundary are not proportional (see (8)), and so one might worry about the integrability of the boundary terms . However, as explained in Perez:2016vqo , since the Lagrange multipliers in (14) are given by the variation of a functional (see (17)) the boundary terms can be explicitly integrated as
Therefore, the suitable action principle for the boundary conditions of KdV-type is precisely identified, and so we are able to proceed with its Hamiltonian reduction.
The constraint is locally solved by . For the sake of simplicity, we disregard non-trivial holonomies, so that can be assumed to be periodic in . Thus, replacing back in the action (29), a straightforward calculation yields
The first two terms naturally appear in the standard chiral WZW action Elitzur:1989nr , but here we have an explicit modification due to the presence of . As shown below, the form of makes possible to recover the infinite-dimensional Abelian algebra in (22) from a Noether symmetry of the full action. Furthermore, note that do not appear to be expressible locally in terms of the group elements .
In order to reduce to a boundary integral, we use the Gauss decomposition for
Here , and are functions of . Thus, can be expressed as
where prime denotes derivatives with respect to . Thus, the action has now been reduced to an integral at the boundary.
which can be further simplified by performing the Gauss decomposition for the group element
where the fields , and depend only on and . Thus, we obtain
and hence, the action (32) reduces to
Besides, the asymptotic form of is determined by eq. (8), so that
which by virtue of the Gauss decomposition (38), implies the following relations
Making use of the first equation in (43), it is straightforward to see that the second term in (41) becomes a total time derivative that can be discarded. The remaining equations in (43) then allow to obtain a crucial relationship, given by
from which the reduced action (41) can be expressed exclusively in term of two fundamental fields .
In sum, the action of the dual theory at the boundary explicitly reads
For the remaining steps, it is worth highlighting that the action (46) possesses the following gauge symmetry
where stand for arbitrary functions. Indeed, under (47), the kinetic term in (46) just changes by a time derivative, while the Hamiltonian does not give additional contributions since only involves angular derivatives of .
3.2 : chiral bosons
in agreement with the standard result obtained in Coussaert:1995zp . The theory describes the dynamics of two chiral bosons of opposite chirality. The field equations in this case then read
which can be readily integrated once, yielding
where are arbitrary functions of time. Therefore, these arbitrary functions can be set to zero by virtue of the gauge symmetry in (47), with , and hence
Note that, as mentioned in the introduction, the field equations for in (51) coincide with the ones of the Virasoro modes in (1). As it is shown below, in our context, the fact that the field equation is equivalent to the conservation law it is actually an accident of the particular case .
3.3 : pmKdV movers
The next case corresponds to the choice so that . The chiral copies of the actions then read
and the field equations are given by
As in the previous case, the equation can be integrated once, giving
where the arbitrary integration function has been set to zero by virtue of an appropriate gauge choice. This equation corresponds to two copies of the pmKdV equation.555The name stems from the fact that under the identification , equation (53) reduces to modified KdV (mKdV) for .
3.4 Generic : pmKdV hierarchy
The field equations can be readily obtained in a closed form for a generic value of , yielding
As in the previous cases, these equations can be integrated once, and by means of the gauge symmetry of the action (47), they reduce to
in agreement with –th representative of the potential form of the mKdV hierarchy.
In the next section it is shown that these equations can be manifestly seen to be integrable, since they admit an infinite number of commuting conserved charges.
4 Symmetries of the action
This section is devoted to study the symmetries and conserved quantities of the action (46). Apart from the gauge symmetry (47), the action (45) also possesses global and kinematic symmetries, which are described in what follows.
4.1 Global symmetries
Here we show that the action (45) is invariant under the following Noether symmetries
with given by (18). It is worth stressing that these global symmetries are in one to one correspondence with the asymptotic symmetries in the bulk. Indeed, by means of the map in (44), the transformation law of that is given by (12) is precisely recovered from (57). Therefore, the corresponding infinite number of commuting Noether charges can be seen to coincide with the surface integrals that come from the analysis in the bulk.
This can be explicitly shown as follows. For each copy of the action (45), the Hamiltonian is invariant under transformation (57), while the kinetic term changes by a total derivative in time. Indeed, equations (12) and (18), imply that the variation of the Hamiltonian term can be expressed as
and hence the transformation (57) is a symmetry of the action. Therefore, the straightforward application of Noether’s theorem yields an infinite number of commuting conserved charges given by
which implies that the field equations in (56) correspond to an integrable system. Besides, and noteworthy, the Noether charges associated with the global symmetries of the dual theory in (60) precisely agree with the surface integrals found from the asymptotic symmetries in the bulk (20).
4.2 Kinematic symmetries & Lifshitz scaling
The kinematic symmetries of the dual action (45) correspond to rigid displacements in space and time, as well as global anisotropic scaling. These symmetries are spanned by a two-dimensional vector field
with , and constants, and is related to the integer through . Under an infinitesimal diffeomorphism spanned by the scalar fields transform as , which implies that left and right Hamiltonians change according to
so that under anisotropic scaling they have weight given by .
It is simple to prove that the dual action (46) is invariant under the symmetries spanned by , and hence, the corresponding Noether charges for the chiral copies are given by
Thus, for each copy, the energy, the momentum, and the conserved charge associated to anisotropic scaling are given by
respectively. Note that correspond to left and right copies of the generator of anisotropic Lifshitz scaling of the form,
so that stands for the dynamical exponent. For each copy, the generators of the kinematic symmetry then fulfill the Lifshitz algebra in two dimensions (see e. g.
Hartnoll:2009sz ; Gonzalez:2011nz ; Taylor:2015glc ). In fact, as it can be readily obtain from relation (21),
one obtains 666In order to recover the Lifshitz algebra, it is useful to make use of the following identity McKean1975 ; 0036-0279-31-1-R03 ; Gelfand:1975rn :
In summary, the only non-vanishing commutators of the infinite set of global symmetries are given by
which means that the conserved charges transform with weight under anisotropic scaling, in agreement with (62).
5 Concluding remarks
We have performed a Hamiltonian reduction of General Relativity in 3D with negative cosmological constant in the case of a new family of boundary conditions, labeled by a non negative integer , which are related to the KdV hierarchy of integrable systems. We then obtained the action of the corresponding dual theory at the boundary, being such that the chiral copies of the reduced system evolve according to the potential form of the modified Korteweg–de Vries equation (56).
The asymptotic symmetries in the bulk are then translated into Noether symmetries of the dual theory, giving rise to an infinite set of commuting conserved charges, that imply integrability of the system. Remarkably, the dual action is also invariant under anisotropic Lifshitz scaling with dynamical exponent .
It is worth pointing out that, if left and right copies were chosen according to different members of the hierarchy, the dual action turns out to be given by
where is defined in (44). The anisotropic scaling symmetry would then be generically broken unless .
It is interesting to make an interpretation of our work in the context of the fluid/gravity correspondence Rangamani:2009xk ; Hubeny:2010wp ; Bredberg:2011jq . In that setup, the asymptotic behavior of the Einstein equations, in a derivative expansion at the boundary, implies that the fluid equations are recovered from the conservation of the suitably regularized Brown-York stress-energy tensor. It is then natural to wonder about the fundamental degrees of freedom and the precise form of the theory from which the fluid is made of.
In our context, since Einstein gravity in 3D is devoid of local propagating degrees of freedom, the identification of the fundamental degrees of freedom at the boundary can be completely performed. Indeed, the asymptotic behavior of the Einstein equations, with the boundary conditions in Perez:2016vqo , is such that they reduce to the equations of the KdV hierarchy to all orders, i.e., without the need of performing a (hydrodynamic) derivative expansion at the boundary. Remarkably, the dynamics of the non-linear fluid, that evolves according to the KdV equations, was shown to emerge from the conservation law of left and right momentum densities, where the underlying fields are manifestly unveiled and fulfill the potential modified KdV equations.
As an ending remark, it is worth mentioning that different classes of boundary conditions relating three-dimensional gravity with integrable systems have been proposed in Afshar:2016wfy ; Afshar:2016kjj ; Fuentealba:2017omf ; Melnikov:2018fhb . It would be interesting to explore whether a similar construction, as the one performed here, could be carried out in those cases.
Acknowledgements.We thank Oscar Fuentealba, Wout Merbis, Alfredo Pérez, Miguel Riquelme and David Tempo, for useful discussions and comments. The work of H.G. is supported by the Austrian Science Fund (FWF), project P 28751-N2. The work of J.M. was supported by the ERC Advanced Grant “High-Spin-Grav”, by FNRS-Belgium (convention FRFC PDR T.1025.14 and convention IISN 4.4503.15). This research has been partially supported by FONDECYT grants Nº 1161311, 1171162, 1181496, 1181628, and the grant CONICYT PCI/REDES 170052. The Centro de Estudios Científicos (CECs) is funded by the Chilean Government through the Centers of Excellence Base Financing Program of Conicyt.
Appendix A Gelfand-Dikii polynomials and Hamiltonians
The Gelfand-Dikii polynomials can be constructed from the recurrence relation (15). In our conventions, the first five polynomials are explicitly given by
Their corresponding densities (17) then read
Thus, according to eq. (9), with , the first four equations of the KdV hierarchy are given by
Appendix B pmKdV equations
The first four equations of the potential modified KdV hierarchy read
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- (9) M. Henneaux, A. Pérez, D. Tempo, and R. Troncoso, “Chemical potentials in three-dimensional higher spin anti-de Sitter gravity,” JHEP 12 (2013) 048, 1309.4362.
- (10) C. Bunster, M. Henneaux, A. Pérez, D. Tempo, and R. Troncoso, “Generalized Black Holes in Three-dimensional Spacetime,” JHEP 05 (2014) 031, 1404.3305.
- (11) I. M. Gelfand and L. A. Dikii, “Asymptotic behavior of the resolvent of sturm-liouville equations and the algebra of the korteweg-de vries equations,” Russ. Math. Surveys 30 (1975), no. 5, 77–113. [Usp. Mat. Nauk30,no.5,67(1975)].
- (12) T. Regge and C. Teitelboim, “Role of Surface Integrals in the Hamiltonian Formulation of General Relativity,” Ann. Phys. 88 (1974) 286.
- (13) M. Banados, C. Teitelboim, and J. Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett. 69 (1992) 1849–1851, hep-th/9204099.
- (14) M. Banados, M. Henneaux, C. Teitelboim, and J. Zanelli, “Geometry of the (2+1) black hole,” Phys. Rev. D48 (1993) 1506–1525, gr-qc/9302012.
- (15) M. Rooman and P. Spindel, “Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS(3) gravity,” Nucl.Phys. B594 (2001) 329–353, hep-th/0008147.
- (16) G. Barnich and H. A. González, “Dual dynamics of three dimensional asymptotically flat Einstein gravity at null infinity,” JHEP 05 (2013) 016, 1303.1075.
- (17) G. Barnich and G. Compère, “Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions,” Class. Quant. Grav. 24 (2007) F15, gr-qc/0610130.
- (18) E. Witten, “Quantum Field Theory and the Jones Polynomial,” Commun.Math.Phys. 121 (1989) 351.
- (19) S. Elitzur, G. W. Moore, A. Schwimmer, and N. Seiberg, “Remarks on the Canonical Quantization of the Chern-Simons-Witten Theory,” Nucl.Phys. B326 (1989) 108.
- (20) P. J. Olver, Applications of Lie groups to differential equations, vol. 107. Springer Science & Business Media, 2000.
- (21) J. P. Wang, “A list of 1+ 1 dimensional integrable equations and their properties,” Journal of Nonlinear Mathematical Physics 9 (2002), no. sup1, 213–233.
- (22) S. A. Hartnoll, “Lectures on holographic methods for condensed matter physics,” 0903.3246.
- (23) H. A. González, D. Tempo, and R. Troncoso, “Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes,” JHEP 11 (2011) 066, 1107.3647.
- (24) M. Taylor, “Lifshitz holography,” Class. Quant. Grav. 33 (2016), no. 3, 033001, 1512.03554.
- (25) H. P. McKean and P. van Moerbeke, “The spectrum of hill’s equation,” Inventiones mathematicae 30 (Oct, 1975) 217–274.
- (26) B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, “Non-linear equations of korteweg-de vries type, finite-zone linear operators, and abelian varieties,” Russian Mathematical Surveys 31 (1976), no. 1, 59.
- (27) M. Rangamani, “Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence,” Class.Quant.Grav. 26 (2009) 224003, 0905.4352.
- (28) V. E. Hubeny, “The Fluid/Gravity Correspondence: a new perspective on the Membrane Paradigm,” Class. Quant. Grav. 28 (2011) 114007, 1011.4948.
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- (30) H. Afshar, S. Detournay, D. Grumiller, W. Merbis, A. Pérez, D. Tempo, and R. Troncoso, “Soft Heisenberg hair on black holes in three dimensions,” Phys. Rev. D93 (2016), no. 10, 101503, 1603.04824.
- (31) H. Afshar, D. Grumiller, W. Merbis, A. Pérez, D. Tempo, and R. Troncoso, “Soft hairy horizons in three spacetime dimensions,” Phys. Rev. D95 (2017), no. 10, 106005, 1611.09783.
- (32) O. Fuentealba, J. Matulich, A. Pérez, M. Pino, P. Rodríguez, D. Tempo, and R. Troncoso, “Integrable systems with BMS Poisson structure and the dynamics of locally flat spacetimes,” JHEP 01 (2018) 148, 1711.02646.
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http://www.meshio.com/car-loan-calculator/
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math
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TIPS: Do not use commas when quoting prices in RM.
Nominal versus effective interest rate
The nominal interest rate is the periodic interest rate times the number of periods per year. For example, a nominal annual interest rate of 12% based on monthly compounding means a 1% interest rate per month (compounded). A nominal interest rate for compounding periods less than a year is always lower than the equivalent rate with annual compounding. A nominal rate without the compounding frequency is not fully defined: for any interest rate, the effective interest rate cannot be specified without knowing the compounding frequency and the rate. Although some conventions are used where the compounding frequency is understood, consumers in particular may fail to understand the importance of knowing the effective rate.
Nominal interest rates are not comparable unless their compounding periods are the same; effective interest rates correct for this by “converting” nominal rates into annual compound interest. In many cases, depending on local regulations, interest rates as quoted by lenders and in advertisements are based on nominal, not effective interest rates, and hence may understate the interest rate compared to the equivalent effective annual rate.
The term should not be confused with simple interest (as opposed to compound interest). Simple interest is interest that is not compounded.
If you happen to have a Financial Calculator, you can easily use the following guide to determine your Effective Interest Rate:
For example, you borrowed RM58,000 for your new Toyota VIOS for 5 years, with a nominal interest rate of 3.00%. According to the repayment schedule issued by your bank, you are expected to pay RM1,112.00 monthly for the next 5 years (60 months).
(i) Loan Amount (PV) = 58,000
This value must be positive because you are actually getting RM58,000 from the bank into our pocket.
(ii) Monthly Installment (PMT) = -1,112
This value must be negative because you are going to pay out this amount out from our pocket.
(iii) Repayment period (n) = 60 months
We need to convert this repayment period of 5 years into 60 months because you are paying the installment is in monthly mode.
With the calculator, you just need to punch the numbers in the following order:
Step 1: 58000 PV
Step 2: 1112 (+/-) PMT
Step 3: 5 [Shift] [n]
Step 4: [Comp] [i%]
In this example, you should get a monthly interest rate of 0.47%. Hence, your Effective Interest Rate is 0.47% x 12 = 5.65%. Hence, the difference between the rate advertised by the bank is 5.65% – 3.00% = 2.65% (Oops!).
Other Useful Tools
To find out how much you will be paying for your road tax, check out Malaysia Road Tax Rate.
To calculate your vehicles insurance premium, use the Motor Insurance Premium Calculator.
To apply or renew your car insurance, head over to InsuranceOnline.my.
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https://www.engineersedge.com/engineering-forum/showthread.php/3564-160-in-the-formula-of-weight-calculation-of-s-steel-blank?s=1825fe14985b2e958983fa06e9a1fb46
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Pls. let me know that how the 160 (or) 160000 is used to find the weight of s.steel blank?.
I saw a methode to find weight of steel blank.
This is the formula: Dia x Dia x Thick/160
How did 160 come?
Pakirmohd, what units do you work in for length and weight?
The equation for weight of a cylinder (i.e. circular blank) is:
Weight = (3.14*D*D/4)*(thickness)*(density)
The 160 probably comes from simplification of:
a) pi (3.14)
c) the density of steel
d) any unit conversions.
I do not believe that the given equation can be assumed to be a valid general equation for determining tubing weights; because the substitution of D*d to replace "(D^2 - d^2)" in a the standard equation: (D^2 - d^2) * pi/4 * t (thickness of the plate) for the volume of metal in a cylinder is not valid.
The only way I can see the above equation being valid is if it is for a specific O.D. I.D. ratio tube; where, for example, d = D/2 and the 2 is one of the factors included in the 160 divisor value.
The D*D in above equation is only the equivalent of D^2 in the standard formula: D^2 * pi/4 * t for the volume of metal in a solid round bar.
I also performed trials using the standard density for a number of metals in the equation and none resulted in the 160 divisor value.
The equation I presented is only valid for a solid steel blank, see attached picture.
Pakirmohd, what units are you using for this equation? Meters? centimeters? millimeters? Inches? And for weight... Pounds? kilograms?
Pakirmohd, please forgive my confusion, while I realize the correct geometrical term for a solid cylindrical shape is a "cylinder", in the ********** in which I have worked this term is principally utilized to indicate a tubular item and "round bar" is the term used to identify a solid cylinder of material.
1/160 = 0.0063 as a multiplier and I cannot find a single material units of density that will convert this to the generally acceptable density value of .283 lb/ft^3 or 489 lb/ft^3 for basic steel.
In addition to Will1234's request for the units, can you also attach a copy of the original document giving this equation?
It's great answer with perfect calculation.
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https://cris.tau.ac.il/en/publications/sampled-data-observers-for-semilinear-damped-wave-equations-under-2
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math
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Sampled-data observers/controllers under sampled measurements were suggested in the past for parabolic systems. In the present paper, for the first time, a sampled-data observer is constructed for a hyperbolic system governed by 1D semilinear wave equation with viscous damping. The measurements are sampled in space and time. Sufficient conditions for the exponential stability of the estimation error system are derived by using the time-delay approach to sampled-data control and an appropriate Lyapunov-Krasovskii functional. The presented numerical examples including observer design for unstable damped sine-Gordon equation illustrate the efficiency of the method.
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https://projecteuclid.org/euclid.aos/1176347131
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math
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The Annals of Statistics
- Ann. Statist.
- Volume 17, Number 2 (1989), 643-653.
On Permutation Tests for Hidden Biases in Observational Studies: An Application of Holley's Inequality to the Savage Lattice
Randomized experiments and observational studies both attempt to estimate the effects produced by a treatment, but in observational studies, subjects are not randomly assigned to treatment or control. A theory of observational studies would closely resemble the theory for randomized experiments in all but one critical respect: In observational studies, the distribution of treatment assignments is not known. The problems that are special to observational studies revolve around our uncertainty about how treatments were assigned. In this connection, tools are needed for describing distributions of treatment assignments that do not assign equal probabilities to all assignments. Two such tools are a lattice of treatment assignments first studied by Savage and an inequality due to Holley for probability distributions on a lattice. Using these tools, it is shown that certain permutation tests are unbiased as tests of the null hypothesis that the distribution of treatment assignments resembles a randomization distribution against the alternative hypothesis that subjects with higher responses are more likely to receive the treatment. In particular, these tests are unbiased against alternatives formulated in terms of a model previously used in connection with sensitivity analyses.
Ann. Statist., Volume 17, Number 2 (1989), 643-653.
First available in Project Euclid: 12 April 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Observational studies permutation test lattice theory Holley's inequality decreasing in transposition decreasing reflection function rank sum test signed rank test Mantel-Haenszel test McNemar-Cox test unbiased test
Rosenbaum, Paul R. On Permutation Tests for Hidden Biases in Observational Studies: An Application of Holley's Inequality to the Savage Lattice. Ann. Statist. 17 (1989), no. 2, 643--653. doi:10.1214/aos/1176347131. https://projecteuclid.org/euclid.aos/1176347131
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http://van.physics.illinois.edu/qa/listing.php?id=164
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math
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Most recent answer: 02/21/2017
Why do heavy and light objects fall at the same speed?
How fast something falls due to gravity is determined by a number known as the "acceleration of gravity", which is 9.81 m/s^2 at the surface of our Earth. Basically this means that in one second, any object
's downward velocity will increase by 9.81 m/s because of gravity. This is just the way gravity works - it accelerates everything at exactly the same rate.
What you may be getting confused by is the fact that the force
of gravity is stronger on heavier objects than lighter ones. Another way of thinking of this is to say that gravity has to pull harder on a heavy object than a light one in order to speed them both up by the same amount.
However, in the real world, we have things like air resistance, which is why sometimes heavy things do fall faster. For example, if you drop a feather and you drop a rock, the rock will land first since the feather is slowed down more by the air. If you did the same thing somewhere where there is no air, the feather and the rock would land at exactly the same time.
p.s. Although Galileo noticed that different things fall at the same rate, there was really no explanation of why until General Relativity was developed. If you would like us to try to say something about how that explanation works, we could make an attempt. mike w
(published on 10/22/2007)
Follow-Up #1: Why fixed gravitational acceleration?
So the force of gravity pulls harder on heavier objects, and it pulls every object no matter what the mass (neglecting air resistance) toward the Earth with enough force to have it accelerate 9.81 m/s/s. But what i don't understand is how this force changes. Like how does gravity "know" how hard it needs to pull the object to make it go 9.81 m/s/s faster. And also, why does Earth have gravity and other objects do not?
- Will (age 18)
Let me take your second question first. It's not true that other objects lack gravity. According to Newton's theory of universal gravitation (published in 1687) absolutely every object exerts a gravitational pull on every other object. The Earth's gravity is most noticeable around here because the Earth is big. Smaller objects have smaller effects. The first direct measurement of the gravitational force between two small objects in a lab was published by Cavendish in 1798.
Now we get to the trickier issue- why the gravitational acceleration depends only on the position of an object, not on its size or what it's made of. Although this was described by Galileo in about 1590, it wasn't explained until Einstein developed general relativity in 1916. Gravity is most accurately described not as a force but as a warping of the spacetime within which all things move. Each object at a particular place and time sees the same warped spacetime. If you try to describe the motion as if it were occurring in Newton's flat spacetime, as we like to do, you get the same acceleration for any slow-moving objects, because that acceleration really just is a measure of the same spacetime curvature.
(published on 01/03/2013)
Follow-Up #2: curving spacetime
Let's say e=mc^2. That would mean that the more mass i have, the more energy i have. Since spacetime is bent by energy, i can bend spacetime more than a feather and therefore i should be able to accelerate faster to earth. Why is that wrong?
- Smith (age 13)
This is the relativistic version of a classical question which we just got around to. (see other follow-ups)
The collision of you and the earth mainly comes from the big spacetime warping due to the earth, not the little warping due to you. However, you do a little warping yourself, and that does show up in the earth's trajectory. The feather does less. So, as you say, even ignoring air friction you and the earth would collide just barely sooner than a feather and the earth, if dropped from the same height.
(published on 01/30/2013)
Follow-Up #3: Earth falling toward you
If you define "falling" as "the closing rate between two objects freely accelerating toward each other", assume everything is done in a perfect vacuum, then when comparing dissimilarly-weighted objects A and B and their closure rate toward the Earth, won't the heavier object actually fall faster?
The acceleration imparted on objects A and B by the Earth is constant, close to 9.8m/s/s. But A and B themselves also impart acceleration on the Earth--minusculely so, but nonetheless so. If you now learn that A is a marble, and B is a marble with our sun compressed inside of it, will B *still* "fall toward the Earth" at the same rate as A?
- Erik E (age 40)
Monterey, CA, USA
Whoops, this is one of those good questions that somehow fell through the cracks long ago. Everything you say is correct. The collision will be a tad sooner for the the heavy object, because the earth accelerates a tiny bit more toward it.
(published on 07/26/2012)
Follow-Up #4: heavier falls faster?
This one guy told me that given enough time a heavier objet would game more speed like if it was dropped from orbit. But I don’t think that’s true, is it?
He also said if you throw the two objects the heavy will hit first. but I think that has more to do with the angle and force you throw it with than gravity’s pull on them.
Do think I’m right? It’s part of a bet. Thank you.
- jon epperson (age 30)
kennewic wa benton
This too slipped through the cracks. I think the answer to the other follow-up should cover it. In practice, of course, what you notice is that air friction makes less difference for the heavier object.
(published on 08/07/2012)
Follow-Up #5: falling objects pulling on Earth
In the answer to Follow-up #3, you said 'The collision will be a tad sooner for the the heavy object, because the earth accelerates a tiny bit more toward it'. How is that? Let the original distance between the objects and Earth be h. Suppose Earth moves towards the heavy object by a distance 'x' due to the heavy object's force, the heavy object has to travel (h-x) before they collide. But then shouldn't the lighter object (ignoring its gravitational force on earth) ALSO travel only (h-x) since the heavier object has already brought Earth x closer to both of them?
- Jayadev Vijayan (age 19)
Chennai, Tamil Nadu, India
Yes, if both objects are dropped together then they hit the Earth at the same time. If they are dropped at different times, the heavy one is just a tiny bit quicker to hit the Earth because it pulls the Earth toward it more.
(published on 03/23/2013)
Follow-Up #6: times for different falling objects
Following up in follow up #5.
That depends on the relative position of the objects.
For instance if the objects are dropped simultaneously on opposite sides of the earth then the lighter object has to travel even farther (h + x) while the heavier only traveled h.
OTOH, if the objects are dropped side by side with, let's say, the heavier object to the left, then the earth would be pulled slightly to the left and thus the heavier object again reaches the earth first.
- Abe (age 49)
Yes, that all sounds right.
(published on 10/06/2013)
Follow-Up #7: Gravitatonal attraction of two unequal mass objects
If two objects having same volume and shape but different masses, then which object will move towards the other or vice-versa or will both the objects move towards each other exactly the same distance?
- Tathagat Bhatia (age 15)
There is an equal and opposite force on each of the two objects: they will both move. Now since the acceleration of each object is inversely proportional to the mass, the lighter object will move a bit faster. If you do the arithmetic you will find that they will meet at their common center of mass. The lighter one will move a bit further than the heavier one.
(published on 10/31/2013)
Follow-Up #8: gravity on different weights
For two objects of different masses and densities in a vacuum, say a bowling ball and a feather, wouldn't the bowling ball accelerate slower than the feather due to inertia? If f = ma and gravity is the force acting pretty much equally on each object, shouldn't their different masses facilitate different accelerations?Thanks
- Nathaniel Scherrer (age 34)
San Diego, California, USA
The acceleration is given by a=F/m. Since F=mg, you get a=g regardless of m.
So, in words, the key point is that the force is not "pretty much equal" on the different objects. It's proportional to their masses. So that means the accelerations are exactly equal.
(published on 07/10/2015)
Follow-Up #9: Newton vindicates Gallileo
In looking for the answer to the question, "Will two objects hit the ground at the same time, regardless of their weight", I found the current webpage and the following sentence from another webpage which seem to contradict each other. This is from the other page: "Heavier things have a greater gravitational force AND heavier things have a lower acceleration. It turns out that these two effects exactly cancel to make falling objects have the same acceleration regardless of mass." Is this true? If so, won't two objects hit the ground at the same time, differences in air displacement not considered?
- Father (age 55)
In the absence of air friction both heavy and light objects will reach the ground at the same time.
Galileo deduced this by devising clever experiments with balls rolling down inclined planes. Newton gave it his blessing by observing that a = F/M, i.e. the acceleration of an object is proportional to the force, F, on it divided by its mass, M. Furthermore the gravitational force on said object was proportional to its mass, F=Mg where g is the measurable acceration of a mass due to gravity on earth. Putting these two equations together you get a = Mg/M = g. The acceleration is independent of mass.
For more information see: https://van.physics.illinois.edu/qa/listing.php?id=164
(published on 02/21/2017)
Follow-up on this answer.
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https://www.thenakedscientists.com/forum/index.php?topic=28175.0
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math
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0 Members and 2 Guests are viewing this topic.
It's a good question, I don't know how to calculate the answer.
Hi geezerI have the mathematical skills of a red cabbage.PS from Red Cabbage: The chemical energy of the propane remains roughly the same in both cool and warm air. That energy is used to overcome the 'heat energy' of the surrounding air. Cool weather might be doing the balloonist a favor by reducing the heat energy of the surrounding air. If that is the case - and insulating capacity of the balloon material remains the same - then less heat energy might be needed to create the differential?Of course my next scientific breakthrough is to simply ask a hot air balloonist. But how much fun would THAT be!
HOW MUCH CAN A BALLOON LIFT? It depends on how cold the air is and the size of the balloon. Balloons lift better in cold air than in warm air. The larger the air volume of the balloon, the more it can lift.
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https://gradestack.com/Complete-CAT-Prep/-My-grandfather-owned/2-39757-19147-3883-test-wtst
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My grandfather owned plenty of land, which easily encompassed an area of 1000 × 200 m2. He wanted to give some part of it to his servant Ramu. But he did not gift it directly. He supplied the material that could form a fence of length 100 m only. Then he allowed Ramu to take any part with four sides that could be encased with the help of the given fencing material.
Ramu had intimate knowledge of the land. Hence, he selected the site having a natural fencing of rocks on one side, because he could utilize the given material only on three sides of the plot. What is the maximum possible land that Ramu can claim now?
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http://www.science.ca/askascientist/viewquestion.php?qID=1333
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Physics Question #1333
Fern Marques, a 60 year old male from North Bay, Ontario asks on March 19, 2003,
How can planetary angular momentum be tranferred from one body (Earth's rotation) to another (Moon's translation around the Earth) by gravity alone? The Earth is slowing down due to tidal movements and the Moon is getting further away. The only connection between the two is gravity... How?
viewed 13695 times
Gravity cannot transfer angular momentum between spherically symmetric bodies. However, the attractive force of the Earth and Moon, because it acts most strongly on the directly adjacent parts (and least strongly on the backsides of each) deforms these slightly elastic bodies -- and in addition causes tidal flows of the liquids in the Earth's oceans. The resulting "bulge" is not symmetric about the Earth-Moon line, but rather is advanced further around the Earth's spin axis by the Earth's rotation. The Moon then sees a gravitational field which has an extra lump on the side of the Earth spinning away from it. The additional attraction of this lump, the result of the tidal bulge shifted by rotation, exerts a torque on the Earth's rotation, slowing it, and a torque on the Earth-Moon system, shifting the Moon to a further orbit.
Add to or comment on this answer using the form below.
Note: All submissions are moderated prior to posting.
If you found this answer useful, please consider making a small donation to science.ca.
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http://oxfordindex.oup.com/view/10.1093/oi/authority.20110803100131949
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math
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A test suitable for testing the null hypothesis of independence between two dichotomous variables using data from a population subdivided into L classes: it is, therefore, a test for use with a 2×2×L contingency table. The test, which was introduced in 1959 by Mantel and Haenszel, is most used in medical contexts where, for example, one variable is outcome (‘success’ or ‘failure’), one variable is treatment (‘control’ or ‘new’), and the L classes correspond to different patient categories. The test assumes that any association between the dichotomous variables is unaffected by the third variable.
The test statistic, M, is computed as follows. Denote by fjkl the number of patients in class l (=1, 2,…, L) who experience outcome j (=1 or 2) when given treatment k (=1 or 2). Write f0kl=f1kl+f2kl, fj0l=fj1l+fj2l, and f00l=f10l+f20l. Then . Under the null hypothesis, the distribution of M is approximated by a chi-squared distribution with one degree of freedom. When L=1 the test is equivalent to the Yates-corrected chi-squared test. The ½ term is a continuity correction.
The test combines information from each of the L classes. In a similar way, the Mantel–Haenszel statistic, ψ, combines information about the strength of the relationship between the dichotomous variables. This statistic, given by , is an aggregate estimate of the odds ratio for the two variables.
Subjects: Probability and Statistics.
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http://betterer.failedrobot.com/index.php/books/free-ideal-rings-and-localization-in-general-rings
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math
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Free Ideal Rings and Localization in General Rings by P. M. Cohn
By P. M. Cohn
Proving polynomial ring in a single variable over a box is a significant excellent area might be performed by way of the Euclidean set of rules, yet this doesn't expand to extra variables. despite the fact that, if the variables should not allowed to go back and forth, giving a unfastened associative algebra, then there's a generalization, the susceptible set of rules, which might be used to turn out that every one one-sided beliefs are loose. This booklet provides the speculation of unfastened perfect jewelry (firs) intimately. there's additionally an entire account of localization that's taken care of for basic earrings however the good points bobbing up in firs are given particular recognition.
Read Online or Download Free Ideal Rings and Localization in General Rings PDF
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The contents of this booklet were used in classes given by way of the writer. the 1st used to be a one-semester path for seniors on the college of British Columbia; it used to be transparent that strong undergraduates have been completely able to dealing with effortless workforce conception and its software to easy quantum chemical difficulties.
Additional resources for Free Ideal Rings and Localization in General Rings
Thus r ≤ m, and by successive cancelling we find that P ∼ = R m−r ; in particular, when r = m, it follows that P = 0. Hence R is n-Hermite. Now the rest follows from (a) by duality. 2. For any non-zero ring the following conditions are equivalent: (a) R is an Hermite ring, ∼ R m−1 , (b) if P ⊕ R ∼ = R m , then P = (c) if P ⊕ R r ∼ = R m−r . 3. An integral domain R is 2-Hermite if and only if, for any right comaximal pair a, b, a R ∩ b R is principal. 22 Generalities on rings and modules Proof. If a, b are right comaximal, then the mapping μ : (x, y)T → ax − by is a surjective homomorphism of right R-modules 2 R → R, giving rise to the exact sequence μ 0 → P −→ 2 R −→ R → 0 .
1 hold in most rings normally encountered, and counter-examples belong to the pathology of the subject. By contrast, the property defined below forms a significant restriction on the ring. Clearly any stably free module is finitely generated projective. If P ⊕ R m is free but not finitely generated, then P is necessarily free (see Exercise 9). In any case we shall mainly be concerned with finitely generated modules. A ring R is called an Hermite ring if it has IBN and any stably free module is free.
Show that a matrix is stably associated to I if and only if it is a unit; if it is stably associated to an m × n zero matrix, where m, n > 0, then it is a zero-divisor. 2. Let A be a matrix over any ring R. Show that the left R-module presented by A is zero if and only if A has a right inverse. 3. Let R be a ring and A ∈ mR n , B ∈ nR m . Show that I + AB is stably associated to I + B A. Deduce that I + AB is a unit if and only if I + BA is; prove this directly by evaluating I − B(I + AB)−1 A. 4◦ .
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https://customessayswriters.net/blogs/a-company-that-produces-pleasure-boats-has-decided-to-expand-one-of-its-lines-current-facilities-are-insufficient-to-handle-the-increased-workload-so-the-company-is-considering-three-alternatives-a/
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A company that produces pleasure boats has decided to expand one of its lines. Current facilities are insufficient to handle the increased workload, so the company is considering three alternatives, A (new location), B (subcontract), and C (expand existing facilities).
Alternative A would involve substantial fixed costs but relatively low variable costs: fixed costs would be $250,000 per year, and variable costs would be $500 per boat. Subcontracting would involve a cost per boat of $2,500, and expansion would require an annual fixed cost of $50,000 and a variable cost of $1,000 per boat.
|a.||Find the range of output for each alternative that would yield the lowest total cost.|
|b.||Which alternative would yield the lowest total cost for an expected annual volume of 150 boats?
Tasks a. and b. have to follow these steps:
Step 1. Determine the tital cost equiation for each alternative.
Step 2. Graph the alternatives
Step 3. Determine over what range each alternative is preffered.
|c.||What other factors might be considered in choosing between expansion and subcontracting?
d. Rework Problem 4b using this additional information: Expansion would result in an increase of $70,000 per year in transportation costs, subcontracting would result in an increase of $25,000 per year, and adding a new location would result in an increase of $4,000 per year.
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https://encyclopedia2.thefreedictionary.com/MMI+code
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math
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MMI code | Article about MMI code by The Free Dictionary
Also found in: Medical
MMI code(Man Machine Interface code) A cellphone code that begins with a star/hash (*#) prefix. MMI codes are entered like telephone numbers to obtain a variety of information as well to enable and disable various actions. For example, entering *#06# on a GSM phone displays the model and serial number (see IMEI).
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https://wisdominnature.org.uk/file-ready/probability-and-statistical-inference-9th-edition
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math
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This text while nearly identical in instruction to probability and statistical inference ninth edition has slightly different problems if you are looking for a textbook to follow along with course content id recommend it but if youre needing to turn in homework from the book unfortunately this is not a good solution. Probability and statistical inference. Probability and statistical inference 9th edition dale zimmerman joins the two leading statistician authors in this edition heis the robert v hogg professor in the department of statistics and actuarial science at the university of iowa. How is chegg study better than a printed probability and statistical inference 9th edition student solution manual from the bookstore our interactive player makes it easy to find solutions to probability and statistical inference 9th edition problems youre working on just go to the chapter for your book. Abebookscom probability and statistical inference 9th edition 9780321923271 by hogg robert v tanis elliot zimmerman dale and a great selection of similar new used and collectible books available now at great prices
How it works:
1. Register Trial Account.
2. Download The Books as you like ( Personal use )
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http://www.studymode.com/essays/Algebra-4-1723361.html
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math
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Introduction to Algebra (MAT 221)
Apr 14, 2013
Algebra Problem Week 5
Buried treasure. Ahmed has half of a treasure map,which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is x?
The Pythagorean Theorem states to find the missing side of a right triangle you can square to know lengths and add the two together. The result will be the distance of the missing length squared.
We know that Ahmed has a map with a distance to the treasure of 2x+6.
We know that Vanessa has a map with a distance of 2x+4, after walking x paces north.
We are looking to solve for the number of paces north Vanessa must walk.
(number of paces north)^2+ (Vanessa’s distance)^2=(Ahmed’s distance)^2
Substituting known variables
x^2 +(2x+4)^2 =(2x+6)^2
Squaring the known variables
x^2 +(2x+4)(2x+4)= +(2x+6)(2x+6)
Multiplying out the compound equation
x^2 +(4x^2+8x+8x+16)= (4x^2+12x+12x+36)
x^2 +(4x^2+16x+16)= (4x^2+24x+36)
Now we have a quadratic equation to solve by factoring and using the zero factor.
(x – ) (x + ) = 0
Since the coefficient of x2 is 1 we can start with a pair of parenthesis with an x in each. Since the 20 is negative we know there will be one + and one – in the binomials. We need two factors of -20 which add up to -8. -1, 20; -2, 10; -4, 5; -5, 4; -10, 2; -20, 1
-10 and 2 will work
(x – 10)(x + 2) = 0 Use the zero factor property to solve each binomial, x – 10 = 0 or x + 2 = 0 creating a compound equation. x = 10 or x =...
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https://marcofrasca.wordpress.com/2011/04/
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math
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Marco Ruggieri is currently a post-doc fellow at Yukawa Institute for theoretical physics in Kyoto (Japan). Marco has got his PhD at University of Bari in Italy and spent a six months period at CERN. Currently, his main research areas are QCD at finite temperature and high density, QCD behavior in strong magnetic fields and effective models for QCD but you can find a complete CV at his site. So, in view of his expertize I asked him a guest post in my blog to give an idea of the current situation of these studies. Here it is.
It is well known that Quantum Chromodynamics (QCD) is the most accredited theory describing strong interactions. One of the most important problems of modern QCD is to understand how color confinement and chiral symmetry breaking are affected by a finite temperature and/or a finite baryon density. For what concerns the former, Lattice simulations convince ourselves that both deconfinement and (approximate) chiral symmetry restoration take place in a narrow range of temperatures, see the recent work for a review. On the other hand, it is problematic to perform Lattice simulations at finite quark chemical potential in true QCD, namely with number of color equal to three, because of the so-called sign problem, see here for a recent review on this topic. It is thus very difficult to access the high density region of QCD starting from first principles calculations.
Despite this difficulty, several work has been made to avoid the sign problem, and make quantitative predictions about the shape of the phase diagram of three-color-QCD in the temperature-chemical potential plane, see here again for a review. One of the most important theoretical issues in along this line is the search for the so-called critical endpoint of the QCD phase diagram, namely the point where a crossover and a first order transition line meet. Its existence was suggested by Asakawa and Yazaki (AY) several years ago (see here) using an effective chiral model; in the 2002, Fodor and Katz (FK) performed the first Lattice simulation (see here) in which it was shown that the idea of AY could be realized in QCD with three colors. However, the estimate by FK is affected seriously by the sign problem. Hence, nowadays it is still under debate if the critical endpoint there exists in QCD or not.
After referring to this for a comprehensive review of some of the techniques adopted by the Lattice community to avoid the sign problem and detect the critical endpoint, it is worth to cite an article by Marco Ruggieri, which appeared few days ago on arXiv, in which an exotic possibility to detect the critical endpoint by virtue of Lattice simulations avoiding the sign problem has been detected, see here . We report, after the author permission, the abstract here below:
We suggest the idea, supported by concrete calculations within chiral models, that the critical endpoint of the phase diagram of Quantum Chromodynamics with three colors can be detected, by means of Lattice simulations of grand-canonical ensembles with a chiral chemical potential, , conjugated to chiral charge density. In fact, we show that a continuation of the critical endpoint of the phase diagram of Quantum Chromodynamics at finite chemical potential, , to a critical end point in the temperature-chiral chemical potential plane, is possible. This study paves the way of the mapping of the phases of Quantum Chromodynamics at finite , by means of the phases of a fictitious theory in which is replaced by .
Rajan Gupta (2011). Equation of State from Lattice QCD Calculations arXiv arXiv: 1104.0267v1
Philippe de Forcrand (2010). Simulating QCD at finite density PoS (LAT2009)010, 2009 arXiv: 1005.0539v2
M. Asakawa, & K. Yazaki (1989). Chiral restoration at finite density and temperature Nuclear Physics A, 504 (4), 668-684 DOI: 10.1016/0375-9474(89)90002-X
Z. Fodor, & S. D. Katz (2001). Lattice determination of the critical point of QCD at finite T and \mu JHEP 0203 (2002) 014 arXiv: hep-lat/0106002v2
Marco Ruggieri (2011). The Critical End Point of Quantum Chromodynamics Detected by Chirally
Imbalanced Quark Matter arXiv arXiv: 1103.6186v1
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https://raise.calculator.zone/
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math
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After selecting the calculation type in the calculator below, enter the required information and press the calculate button.
- Loss Calculator
- Perimeter Calculator
- Week of Year Calculator
- Weekday Calculator
- Number of Days Between Two Dates Calculator
- Number of Weeks Between Two Dates Calculator
What is a raise?
It literally means an increase in price.
How is the raise calculated?
The increment rate is added to the number 100 and the result is divided by 100. When the result is multiplied by the normal price, an increased price is obtained. For example, if there is a 10% increase in the price of a good whose sales price is USD 500, the new price will be determined as 500 x (100 + 10) / 100 = 500 x 1.1 = USD 550.
How is the raise rate calculated?
The price increase is divided by the normal price and multiplied by 100. Subsequently, the rate of increase is calculated by subtracting the number 100 from the result obtained. For example, if the price of a commodity with a raise price of USD 550 before the increase is USD 500, the increase rate will be calculated as (550/500) x 100 - 100 = 10 (ie 10%).
How is the normal price calculated from the price increase?
The increased price is multiplied by 100 and the result is divided by the addition of the increase rate to 100. For example, a price of USD 550 after a 10% raise is calculated as 550 x 100 / (100 + 10) = USD 500 before an increase is made.
How much is 10 percent raise?
For example, if a 10% increase is made to a person who gets a salary of USD 2,000, the raise amount will be 2000 x 10/100 = USD 200. In other words, the salary of an employee who receives a 10% raise in his / her salary will be calculated as 2000 + 200 = USD 2200.
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https://www.assignmentexpert.com/homework-answers/mathematics/abstract-algebra/question-3284
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math
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Answer to Question #3284 in Abstract Algebra for francis
L = π D = 72π = 226 inches = 18.83 feet.
18/2 = 9 persons can sit around the table at once.
Need a fast expert's response?Submit order
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
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https://socratic.org/questions/a-balloon-has-a-volume-of-253-2-ml-at-356-k-the-volume-of-the-balloon-is-decreas
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math
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A balloon has a volume of 253.2 mL at 356 K. The volume of the balloon is decreased to 165.4 mL. What is the new temperature?
The new temperature is
Charles' law states that when pressure is held constant, temperature and volume are directly proportional. The equation to use is
Rearrange the equation to isolate
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https://cpt.hitbullseye.com/Aricent-Technical-Questions.php
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math
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Consider two strings A = "qpqrr" and B = "pqprqrp". Let x be the length of the longest common subsequence (not necessarily contiguous) between A and B and let y be the number of such longest common subsequences between A and B. Then x +y = ___.
Answer: Option A
Complete Test Series for Wipro Bag your Dream Job Today Comprehensive Online TestsInclusive Prep for All Placement ExamsAcquire Essential Domain Skills
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http://genealogyresources.org/Tazewell.html
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math
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Census Records Military
Other States New Titles E-BOOKS
Iberian Publishing Company's On-Line Catalog:
Tazewell County Virginia
Tazewell County was formed in 1800 from portions of Russell and Wythe counties. The new county was named for Henry Tazewell, United States senator from Virginia from 1794 until his death in 1799. Russell gave an additional parcel to Tazewell in 1807. Logan County, formed in 1824, took its territory from Tazewell. In 1835 a portion of Russell County was added to Tazewell, and in 1836 a single farm was transferred from Tazewell to Giles jurisdiction. The following year, in 1837 Mercer County was created from portions of Tazewell and Giles counties. Buchanan and McDowell counties took additional parts of Tazewell in 1858. After that Tazewell's boundaries reached their current position.
For a better understanding of county boundary changes, see our new section Virginia in Maps
TAZEWELL COUNTY, VA 1810 SUBSTITUTE CENSUS [Abstracts from the 1810 Personal Property Tax List]
by John Vogt, 2011, 5 1/2"x8 1/2" format, viii, 6 pages, map.
Tazewell is one of eighteen Virginia counties for which the 1810 census is lost. In August, 1814 British troops occupied Washington, DC and public buildings were put to the torch. In the destruction that followed, numerous early records of the government were lost, including all of Virginia’s 1790 and 1800 census reports, as well as eighteen county lists for the state's most recent federal census. Although two “fair copies” of each county’s census had been left in the counties for public display, these were ephemeral lists and not preserved, and by 1814 they too had been mislaid, lost, or destroyed. Hence, the closest document available we have to reconstruct a partial image of the missing county lists is the personal property tax list.
According to research notes by Minor T. Weisiger, Library of Virginia archivist:
“Information recorded in Virginia personal property tax records changed gradually from 1782 to 1865. The early laws required the tax commissioner in each district to record in “a fair alphabetical list” the names of the person chargeable with the tax, the names of white male tithables over the age of twenty-one, the number of white male tithables between ages sixteen and twenty-one, the number of slaves both above and below age sixteen, various types of animals such as horses and cattle, carriage wheels, ordinary licenses, and even billiard tables. Free Negroes are listed by name and often denoted in the list as “free” or “FN.”
The present abstract of Tazewell's 1810 personal property tax list is NOT a transcript of the entire document; rather, it is a summary of three items important in delineating the 1810 "substitute" census for this county, i.e., number of male tithables 16 and older, number of slaves twelve years and older, and the number of horses. The original form of the census was in alphabetic order by date and letter [see example on page vi below]. The substitute list presented here is in absolute alphabetic order for easy reference.
In the current volume, the data is recorded thus:
Coleman, Cain 1 - -
Coleman, Obadiah & his sons,
James, John, &
Anderson 4 6 9
Coleman, William &
Coleman, Whitehead 2 21 25
Column one represents the tithable males (16 and over) in the household; column 2 is the number of slaves over 12; and the final column is the number of horses, mares or mules.
For genealogical researchers in this 1810 period, personal property tax records may provide additional important information. Oftentimes, juniors and seniors are listed adjacent to one another and recorded on the same day. When a taxpayer is noted as “exempt”, it can be a clue to someone holding a particular position in government or being elderly, infirm, or for some other reason no longer required to pay the tithable tax. Women, both black and white, appear occasionally as heads of households when they own property in their own right or as the widow of a property owner.
Another valuable source for filling in information about an ancestor is the land tax record, and especially the one for 1815. In that year, the enumerators began to add the location of the property in relation to the county court house. Roger Ward has abstracted all of the 1815 land tax records, and they are available from this publisher at www.iberian.com.
The 1810 substitute census list for Tazewell County contains 453 households, 537 tithables, both white and free black, and 173 slaves over the age of twelve, and 1,751 horses.
SURNAMES included in the 1810 personal property list are:
Adams; Adkins; Allen; Alsup; Arnal; Aronhart; Asbury; Ashbury; Ashby;
Bailey; Balden; Baley; Ballew; Bandy; Barker; Barnet; Barns; Been; Belcher; Belsha; Belsher; Beverly; Bevers; Biggs; Blankenship; Bolen; Bostick; Boswell.; Bowen; Brooks; Brown; Bruster; Burgman; Burriss;
Cambel; Carter; Cartmill; Cassady; Day; Cecil; Christian; Chriswell; Clapole; Clark; Coleman; Conley; Corder; Correl; Crage; Crawford; Crockett; Cumpton;
Daly; Deskin; Davidson; Davis; Day; Deskins; Dills; Doake; Dolsbury; Dotson; Drake;
Fannon; Fletcher; Flummer; Fortner; Fox; Francisco;
Garrison; George; Gibson; Gillespie; Godfrey; Godfry; Golsby; Gooden; Goss; Green; Grenup; Griffith; Griffitts; Grudd;
Hager; Haley; Hall; Hankins; Hanson; Harman; Harman; Harper; Harrison; Harriss; Hartwell; Havens; Hedrick; Helvy; Heninger; Hicks; Higginbotham; Higginbothum; Hinkle; Hortain; Husk;
Jeffry; Jent; Johnston; Jones; Justice;
Kidd; Kindle; Kindrick; King; Kirk; Kook;
Laird; Lambert; Lasley; Lee; Lester; Likens; Lockhart; Lortain; Lusk; Luster;
Marlow; Mars; Martain; Matney; Maxwell; McCurdy; McDowel; McGuire; Mclngtosh; McMillin; Meloney; Merman; Messersmith; Milum; Mitchel; Moor; Morgan; Murry;
Neel; Newton; Nuckels;
O'Danold; Oney; Ony; Owens;
Patten; Peery; Perry; Pleasant; Power; Prater; Pruet; Pruett;
Ratliff; Reignhart; Reyburn; Right; Robinson; Runnion;
Sanders; Sawyers; Shannon; Shortridge; Simpson; Skaggs; Slater; Smith; Smythe; Steel; Stephenson; Stiltner; Stobauck; Stowers; Stump; Suiter; Suter; Swader;
Taylor; Thompson; Thorn; Tifney; Todd; Tomblenson; Totten; Trent; Trout; Turner;
Vandyke; Vincel; Vinsle;
Waggoner; Walls; Ward; Webb; Weltch; Whit; White; Whitley; Williams; Wilson; Wilton; Witten; Workman; Wynne;
Also available as a digital e-book in PDF format: HOW TO ORDER
SELECTED DEATH RECORDS OF SOUTHWEST VIRGINIANS WHO DIED IN MISSOURI (OR WERE RELATED TO THOSE WHO DIED IN MISSOURI (with additions from Iowa and Sullivan County/East Tennessee)
Researched by Thomas Jack Hockett; Abstracted & compiled by by Donald W. Helton. iv,220pp., every-name index (8.25" x 10.75" paperback). These deaths are taken from a variety of sources and methods employed, including "hunt and seek", census, on-line sources at Rootsweb, Ancestry, IGI, Family Genealogy Forums, censuses, etc. and the very valuable Missouri Death Certificates 1912-1958 which are generously available online. These deaths of mid and extreme SW VA people in MO during the subject time likely represent only a fraction of the deaths which could be ferreted out with difficulty employing 2-4 sources (in conjunction) in conjunction. The work represents considerable labor (not to mention eye-strain) and it is hoped it will bolster further the efforts to document the migration of SW VA persons”.
During the process of abstracting and compiling the death records listed herein, instances of conflict occurred between the certificate and additional information found on-line. The information is entered as found. Any such conflicts are left to the discretion of the reader to reconcile.
Table of contents
Missouri Deaths from
Washington County 1
Wythe Co., Va 43
Russell Co., Va 56
Grayson/Carroll Cos., VA 80
Smyth Co., Va 85
Tazewell Co., Va 101
Lee Co., Va 118
Scott Co., Va 138
Dickenson Co., Va 151
Buchanan Co., Va 154
Miscellaneous Deaths from southwest Va. 181
Iowa Deaths from Southwest Virginia 193
Alphabetical Index 202
Tazewell Co. 1815 Directory of Landowners
by Roger G. Ward. 2005. 14 pages, map, 5 1/2X8 1/2.
For a full description of the 1815 LAND DIRECTORY Records and a listing of available counties, see:
Individual County Booklets, 1815 Directory of Virginia Landowners
For records pertaining to Tazewell COUNTY, VIRGINIA see:
|| Virginia/W.Va. || General Reference || Military Records ||
|| Other States || Genealogy Links || New Titles || Home Page || E-Books ||
Copyright © 2014 Iberian Publishing Company
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http://oilf.blogspot.com/2009/11/mitosis-rote-memorization-and.html
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math
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Before mitosis begins, the chromosomes and other cell materials are copied. [are copied? Who or what does the copying???] The pairs of centrioles, which are two cylindrical structures, are also copied. [Besides being cylindrical, what is a centriole, and what is its significance for mitosis???] Each chromosome now consists of two chromatids. [Remind us what a chromatid is!!!]From Cells, Heredity, and Classification (Holt, Rinehart and Winston), with my queries in brackets.
Mitosis Phase 1
Mitosis begins. The nuclear membrane brakes apart. [Why?] Chromosomes condense into rodlike structures. [Why is the new, rodlike structure important and significant?] The two pairs of centrioles move to opposite sides of the cell. [Significance?] Fibers form between the two pairs of centrioles and attach to the centromeres. [Remind us what a centromere is and why it is significant!]
Mitosis Phase 2
The chromosomes line up along the equator of the cell. [How??? and Why???]
Mitosis Phase 3
The chromatids separate [How?] and are pulled to opposite sides of the cell by the fibers attached to the centrioles. [This crucial event should be the centerpiece of the whole discussion of mitosis].
Mitosis Phase 4
The nuclear membrane forms around the two sets of chromosomes, and they unwind. The fibers disappear. Mitosis is complete.
With all the questions it begs and explanations it lacks, this is little more than a list of terms and series of steps to memorize, with no obvious general concepts to guide or interest you. This approach seems to have a long history. It includes my own biology book of a generation ago, which is why I never pursued biology after 9th grade.
But now that my autistic son is studying it in middle school, I need to understand it better.
Only after multiple readings of the passage above did I sort of figure out what the underlying concepts were. (Perhaps if I were a more visual thinker, it wouldn't have taken me so long.)
Assuming that I'm more or less on target, it strikes that a more engaging introduction to mitosis might go somewhere along these lines (ideally generated by some sort of Socratic dialog, with accompanying illustrations):
We already know that cells consist of crucial elements, for example, the mitochondria and the chromosomes. We also know that for organisms to grow, their cells must divide. But is cell division as simple as a cell dividing itself into two? Bear in mind that each "half" of the cell must have all the crucial elements. This means that each element must be copied, and each half must end up with one copy of the element.
Making sure that each "cell half" has exactly one copy of a given element is particularly complicated when it comes to the chromosomes. Is it enough for each chromosome to make a copy of itself? Imagine what would happen if the chromosome copies simply swam around in the cytoplasm while the cell divides. Then what's to stop one half from ending up with two copies of chromosome 1 and no copies of chromosome 2, or vice versa? We already know how each chromosome contains different sets of crucial instructions for the cell, so the results of this kind of lopsided split would be disastrous.
So how can a cell make sure that exactly one copy of each of its dozen or more chromosomes ends up in each "cell half" before the division? Since the cell has no "brain" or other centralized information processor, as soon as the chromosome copy separates from its original, there's no way for the cell to "know" which copy goes with which original, and therefore no way to guarantee that each cell half gets exactly the right number of copies.
Well, suppose each chromosome copy remains attached to the original up until right before the cell divides. This preserves the information about which copy matches up with which original. Then suppose the chromosome pairs (original plus copy) all line up in such away that a simultaneous, symmetrical force emanating from each cell half can pull them apart, so that each original copy ends up in one half while its copy ends up in the other half.
Let's picture how this could happen. Imagine if the chromosome pairs line up along the equator of the cell, with one pair member on each side of the equator. Now imagine tentacles reaching out from the middle of the edge of each cell half and pulling at each chromosome pair from each side. If these tentacles are equally strong, and strong enough to separate the chromosome pairs, the result is just what we want: exactly one copy of each chromosome pulled into each cell half.
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https://www.teacherspayteachers.com/Product/Fractions-Decimals-Percents-with-Ratios-in-Word-Problems-1141067
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math
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This is a powerpoint with 32 slides focusing on percent of numbers, fractions of a number, ratios thinking in fraction form, some decimals all with problem solving. I am trying to get the students to think about the power of estimation first, then making sense of the problem and if they know which operation or strategy to use. Then solve showing work. Every other page has the answers displayed. I am going to time each slide and have a student come up to explain and show their work, then we will advance to the answer slide. This is part of the number sense common core standards. Enjoy and change if necessary.
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https://jimadamsauthordotcom.wordpress.com/2017/12/09/angle-measurement/
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math
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Radians and degrees are two ways of measuring the same thing. Angle measurement can be calculated, in both degrees and radians, but in certain cases radians are more important. There are 360 degrees in a circle and 2π radians in a circle. We usually use fractions with pi when talking about radians, because it is actually easier to work with the fractions. Pi radians translates to 180 degrees and half of that 90° = π/2 = 1.5707964 as a decimal equivalent. Radians are just another form of measurement that can be used to scale things with larger form. Anything that is measured in degrees can also be measured in radians. One degree has a measure of 60 min, and 0.5 degrees is equivalent to 0.5 * 60 = 30 minutes, so 30 minutes is half of one degree.
Our counting and measuring system is based on the number 10, but the Babylonians used a base 60 number system. The number 360 is totally arbitrary, it was chosen simply because the Babylonians preferred multiples of 60. The circumference of a circle ‘C’ is equal to the length of the radius ‘r’ times 2π, thus C = 2πr. Degrees let us work with integers (like 30o) instead of nasty ratios involving irrational numbers (like π/6) and they are easier for most measurements, but Trigonometry marked a turning point in math, and to navigate that terrain, you need a notion of angles that’s more natural, more fundamental, than slicing up the circle into an arbitrary number of pieces. The number π, strange though it may seem, lies at the heart of mathematics. The number 360 doesn’t fit well with pi and radians can take you places that degrees simply can’t.
The new way of teaching trigonometry works with the unit circle, which is a circle that has a radius of ‘one’ and because it is so simple, it has become the new method to learn about lengths and angles. The polar coordinates (r, θ) of the point P, where r is the distance that P is from the origin O and θ (theta) is the angle between the lines Ox and OP, this is shown in the following diagram.
In the Polar Coordinate System, we go around the origin or the pole a certain distance out, and a certain angle from the positive x axis. The ordered pairs, called polar coordinates, are in the form (r, θ), with r being the number of units from the origin or pole (if r > 0), like a radius of a circle, and θ being the angle (in degrees or radians) formed by the ray on the positive x axis (polar axis), going counter-clockwise.
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http://school.bealsscience.com/planetarium
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math
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GEODESIC DOME / PLANETARIUM
Visit the "Planetarium Blog" at:
You will be involved in a project at Senior High where math and science classes will collaborate to build a geodesic dome. Upon completion, the geodesic dome will be used as a planetarium to discover the wonders of the universe in an immersive environment.
Follow the instructions of the webquest and answer the questions:
1. Define "geodesic"
2. Define "planetarium"
3. What is a geodesic dome?
4. Who designed the first geodesic dome? What year? What was it used for?
5. List two structural advantages of a dome.
6. List two disadvantages to building a geodesic dome for a home.
7. List 5 different uses for "mega-sized" geodesic domes by examining the 10 largest in the world
8. According to this website, which "office supplies" would be useful for attaching the different triangles of the geodesic dome together?
9. Using the site above, click on "Dome Calculator" to the left. Click on 3V. See if you can find the assembly diagram for a dome with a radius of 7.5 feet. How many pentagons (5 sided figures) will be needed for construction of this type of dome?
(Hint: Look for the assembly diagram. Think about the diagram in three dimensions because you can only see one side on the diagram.)
This is the website for the Taylor Planetarium at The Museum of the Rockies in Bozeman, MT. Check out the interactive game from the planetarium at:
10. Find Ursa Major by clicking on the various stars. Explain what Ursa Major is.
11. Find Hercules. Explain the constellation.
Print and build the geodesic dome.
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http://hermeneutics.stackexchange.com/questions/tagged/zephaniah?sort=votes&pagesize=15
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math
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Biblical Hermeneutics Meta
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Leaping over the threshold in Zephaniah 1:9
It would seem from the various translations of Zephaniah 1:9 that is is tricky to understand. Some translations give an apparently fairly vanilla, literal rendering: On that day I will punish ...
Jun 22 '12 at 1:54
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https://cdn.loot.co.za/browse/general?cat=dvf&offset=575
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math
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Presents an in-depth analysis of geometry of part surfaces and provides the tools for solving complex engineering problems
"Geometry of Surfaces: A Practical Guide for Mechanical Engineers" is a comprehensive guide to applied geometry of surfaces with focus on practical applications in various areas of mechanical engineering. The book is divided into three parts on Part Surfaces, Geometry of Contact of Part Surfaces and Mapping of the Contacting Part Surfaces.
"Geometry of Surfaces: A Practical Guide for Mechanical Engineers "combines differential geometry and gearing theory and presents new developments in the elementary theory of enveloping surfaces. Written by a leading expert of the field, this book also provides the reader with the tools for solving complex engineering problems in the field of mechanical engineering.Presents an in-depth analysis of geometry of part surfaces Provides tools for solving complex engineering problems in the field of mechanical engineeringCombines differential geometry and gearing theoryHighlights new developments in the elementary theory of enveloping surfaces
Essential reading for researchers and practitioners in mechanical, automotive and aerospace engineering industries; CAD developers; and graduate students in Mechanical Engineering.
This book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest.
This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiri Matousek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition - something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiri Matousek's numerous areas of mathematical interest.
This book is addressed to graduate students and researchers in the fields of mathematics and physics who are interested in mathematical and theoretical physics, differential geometry, mechanics, quantization theories and quantum physics, quantum groups etc., and who are familiar with differentiable and symplectic manifolds. The aim of the book is to provide the reader with a monograph that enables him to study systematically basic and advanced material on the recently developed theory of Poisson manifolds, and that also offers ready access to bibliographical references for the continuation of his study. Until now, most of this material was dispersed in research papers published in many journals and languages. The main subjects treated are the Schouten-Nijenhuis bracket; the generalized Frobenius theorem; the basics of Poisson manifolds; Poisson calculus and cohomology; quantization; Poisson morphisms and reduction; realizations of Poisson manifolds by symplectic manifolds and by symplectic groupoids and Poisson-Lie groups. The book unifies terminology and notation. It also reports on some original developments stemming from the author's work, including new results on Poisson cohomology and geometric quantization, cofoliations and biinvariant Poisson structures on Lie groups.
This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, which explains a more classical view of hyperbolic non-Euclidean geometry in all dimensions. Finally, the author explains a natural intrinsic obstruction to flattening a triangulated polyhedral surface into the plane without distorting the constituent triangles. That obstruction extends intrinsically to smooth surfaces by approximation and is called curvature. Gauss's original definition of curvature is extrinsic rather than intrinsic. The final two chapters show that the book's intrinsic definition is equivalent to Gauss's extrinsic definition (Gauss's "Theorema Egregium" ("Great Theorem")).
This is the first book to present a complete characterization of Stein-Tomas type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to the given surface. Isroil Ikromov and Detlef Muller begin with Elias M. Stein's concept of Fourier restriction and some relations between the decay of the Fourier transform of the surface measure and Stein-Tomas type restriction estimates. Varchenko's ideas relating Fourier decay to associated Newton polyhedra are briefly explained, particularly the concept of adapted coordinates and the notion of height. It turns out that these classical tools essentially suffice already to treat the case where there exist linear adapted coordinates, and thus Ikromov and Muller concentrate on the remaining case. Here the notion of r-height is introduced, which proves to be the right new concept. They then describe decomposition techniques and related stopping time algorithms that allow to partition the given surface into various pieces, which can eventually be handled by means of oscillatory integral estimates. Different interpolation techniques are presented and used, from complex to more recent real methods by Bak and Seeger. Fourier restriction plays an important role in several fields, in particular in real and harmonic analysis, number theory, and PDEs. This book will interest graduate students and researchers working in such fields.
The book faces the interplay among dynamical properties of semigroups, analytical properties of infinitesimal generators and geometrical properties of Koenigs functions. The book includes precise descriptions of the behavior of trajectories, backward orbits, petals and boundary behavior in general, aiming to give a rather complete picture of all interesting phenomena that occur. In order to fulfill this task, we choose to introduce a new point of view, which is mainly based on the intrinsic dynamical aspects of semigroups in relation with the hyperbolic distance and a deep use of Caratheodory prime ends topology and Gromov hyperbolicity theory. This work is intended both as a reference source for researchers interested in the subject, and as an introductory book for beginners with a (undergraduate) background in real and complex analysis. For this purpose, the book is self-contained and all non-standard (and, mostly, all standard) results are proved in details.
Throughout history, thinkers from mathematicians to theologians have pondered the mysterious relationship between numbers and the nature of reality. In this fascinating book, Mario Livio tells the tale of a number at the heart of that mystery: phi, or 1.6180339887...This curious mathematical relationship, widely known as "The Golden Ratio," was discovered by Euclid more than two thousand years ago because of its crucial role in the construction of the pentagram, to which magical properties had been attributed. Since then it has shown a propensity to appear in the most astonishing variety of places, from mollusk shells, sunflower florets, and rose petals to the shape of the galaxy. Psychological studies have investigated whether the Golden Ratio is the most aesthetically pleasing proportion extant, and it has been asserted that the creators of the Pyramids and the Parthenon employed it. It is believed to feature in works of art from Leonardo da Vinci's Mona Lisa to Salvador Dali's The Sacrament of the Last Supper, and poets and composers have used it in their works. It has even been found to be connected to the behavior of the stock market!
While it is well known that the Delian problems are impossible to solve with a straightedge and compass - for example, it is impossible to construct a segment whose length is cube root of 2 with these instruments - the discovery of the Italian mathematician Margherita Beloch Piazzolla in 1934 that one can in fact construct a segment of length cube root of 2 with a single paper fold was completely ignored (till the end of the 1980s). This comes as no surprise, since with few exceptions paper folding was seldom considered as a mathematical practice, let alone as a mathematical procedure of inference or proof that could prompt novel mathematical discoveries. A few questions immediately arise: Why did paper folding become a non-instrument? What caused the marginalisation of this technique? And how was the mathematical knowledge, which was nevertheless transmitted and prompted by paper folding, later treated and conceptualised? Aiming to answer these questions, this volume provides, for the first time, an extensive historical study on the history of folding in mathematics, spanning from the 16th century to the 20th century, and offers a general study on the ways mathematical knowledge is marginalised, disappears, is ignored or becomes obsolete. In doing so, it makes a valuable contribution to the field of history and philosophy of science, particularly the history and philosophy of mathematics and is highly recommended for anyone interested in these topics.
This volume contains the proceedings of the AMS Special Session on Algebraic and Combinatorial Structures in Knot Theory and the AMS Special Session on Spatial Graphs, both held from October 24-25, 2015, at California State University, Fullerton, CA. Included in this volume are articles that draw on techniques from geometry and algebra to address topological problems about knot theory and spatial graph theory, and their combinatorial generalizations to equivalence classes of diagrams that are preserved under a set of Reidemeister-type moves. The interconnections of these areas and their connections within the broader field of topology are illustrated by articles about knots and links in spatial graphs and symmetries of spatial graphs in $S^3$ and other 3-manifolds.
Designed to inform readers about the formal development of
Euclidean geometry and to prepare prospective high school
mathematics instructors to teach Euclidean geometry, this text
closely follows Euclid's classic, "Elements. "The text augments
Euclid's statements with appropriate historical commentary and many
exercises -- more than 1,000 practice exercises provide readers
with hands-on experience in solving geometrical problems.
This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study. The families of geometries covered in this book include among others the generalized polygons, near polygons, polar spaces, dual polar spaces and designs. Also the various relationships between these geometries are investigated. Ovals and ovoids of projective spaces are studied and some applications to particular geometries will be given. A separate chapter introduces the necessary mathematical tools and techniques from graph theory. This chapter itself can be regarded as a self-contained introduction to strongly regular and distance-regular graphs. This book is essentially self-contained, only assuming the knowledge of basic notions from (linear) algebra and projective and affine geometry. Almost all theorems are accompanied with proofs and a list of exercises with full solutions is given at the end of the book. This book is aimed at graduate students and researchers in the fields of combinatorics and incidence geometry.
This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition" "... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty." From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Gunter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdoes. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011
In this book, Cathleen Heil addresses the question of how to conceptually understand children's spatial thought in the context of geometry education. She proposes that in order to help children develop their abilities to successfully grasp and manipulate the spatial relations they experience in their everyday lives, spatial thought should not only be addressed in written or tabletop settings at school. Instead, geometry education should also focus on settings involving real space, such as during reasoning with maps. In a first part of this book, she theoretically addresses the construct of spatial thought at different scales of space from a cognitive psychological point of view and shows that maps can be rich sources for spatial thinking. In a second part, she proposes how to measure children's spatial thought in a paper-and-pencil setting and map-based setting in real space. In a third, empirical part, she examines the relations between children's spatial thought in those two settings both at a manifest and latent level.
This book features a selection of articles based on the XXXIV Bialowieza Workshop on Geometric Methods in Physics, 2015. The articles presented are mathematically rigorous, include important physical implications and address the application of geometry in classical and quantum physics. Special attention deserves the session devoted to discussions of Gerard Emch's most important and lasting achievements in mathematical physics. The Bialowieza workshops are among the most important meetings in the field and gather participants from mathematics and physics alike. Despite their long tradition, the Workshops remain at the cutting edge of ongoing research. For the past several years, the Bialowieza Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented. The unique atmosphere of the Workshop and School is enhanced by the venue, framed by the natural beauty of the Bialowieza forest in eastern Poland.
"Edmund Husserl's Origin of Geometry": An Introduction" (1962) is Jacques Derrida's earliest published work. In this commentary-interpretation of the famous appendix to Husserl's "The Crisis of European Sciences and Transcendental Phenomenology," Derrida relates writing to such key concepts as differing, consciousness, presence, and historicity. Starting from Husserl's method of historical investigation, Derrida gradually unravels a deconstructive critique of phenomenology itself, which forms the foundation for his later criticism of Western metaphysics as a metaphysics of presence. The complete text of Husserl's Origin of Geometry is included.
This open access book focuses on the interplay between random walks on planar maps and Koebe's circle packing theorem. Further topics covered include electric networks, the He-Schramm theorem on infinite circle packings, uniform spanning trees of planar maps, local limits of finite planar maps and the almost sure recurrence of simple random walks on these limits. One of its main goals is to present a self-contained proof that the uniform infinite planar triangulation (UIPT) is almost surely recurrent. Full proofs of all statements are provided. A planar map is a graph that can be drawn in the plane without crossing edges, together with a specification of the cyclic ordering of the edges incident to each vertex. One widely applicable method of drawing planar graphs is given by Koebe's circle packing theorem (1936). Various geometric properties of these drawings, such as existence of accumulation points and bounds on the radii, encode important probabilistic information, such as the recurrence/transience of simple random walks and connectivity of the uniform spanning forest. This deep connection is especially fruitful to the study of random planar maps. The book is aimed at researchers and graduate students in mathematics and is suitable for a single-semester course; only a basic knowledge of graduate level probability theory is assumed.
K3 surfaces are central objects in modern algebraic geometry. This book examines this important class of Calabi-Yau manifolds from various perspectives in eighteen self-contained chapters. It starts with the basics and guides the reader to recent breakthroughs, such as the proof of the Tate conjecture for K3 surfaces and structural results on Chow groups. Powerful general techniques are introduced to study the many facets of K3 surfaces, including arithmetic, homological, and differential geometric aspects. In this context, the book covers Hodge structures, moduli spaces, periods, derived categories, birational techniques, Chow rings, and deformation theory. Famous open conjectures, for example the conjectures of Calabi, Weil, and Artin-Tate, are discussed in general and for K3 surfaces in particular, and each chapter ends with questions and open problems. Based on lectures at the advanced graduate level, this book is suitable for courses and as a reference for researchers.
This book is a monograph on unitals embedded in ?nite projective planes. Unitals are an interesting structure found in square order projective planes, and numerous research articles constructing and discussing these structures have appeared in print. More importantly, there still are many open pr- lems, and this remains a fruitful area for Ph.D. dissertations. Unitals play an important role in ?nite geometry as well as in related areas of mathematics. For example, unitals play a parallel role to Baer s- planes when considering extreme values for the size of a blocking set in a square order projective plane (see Section 2.3). Moreover, unitals meet the upper bound for the number of absolute points of any polarity in a square order projective plane (see Section 1.5). From an applications point of view, the linear codes arising from unitals have excellent technical properties (see 2 Section 6.4). The automorphism group of the classical unitalH =H(2, q ) is 2-transitive on the points ofH, and so unitals are of interest in group theory. In the ?eld of algebraic geometry over ?nite ?elds, H is a maximal curve that contains the largest number of F -rational points with respect to its genus, 2 q as established by the Hasse-Weil boun
This book showcases the synthetic problem-solving methods which frequently appear in modern day Olympiad geometry, in the way we believe they should be taught to someone with little familiarity in the subject. In some sense, the text also represents an unofficial sequel to the recent problem collection published by XYZ Press, 110 Geometry Problems for the International Mathematical Olympiad, written by the first and third authors, but the two books can be studied completely independently of each other. The work is designed as a medley of the important Lemmas in classical geometry in a relatively linear fashion: gradually starting from Power of a Point and common results to more sophisticated topics, where knowing a lot of techniques can prove to be tremendously useful. We treat each chapter as a short story of its own and include numerous solved exercises with detailed explanations and related insights that will hopefully make your journey very enjoyable.
Sasha Wang revisits the van Hiele model of geometric thinking with Sfard's discursive framework to investigate geometric thinking from a discourse perspective. The author focuses on describing and analyzing pre-service teachers' geometric discourse across different van Hiele levels. The explanatory power of Sfard's framework provides a rich description of how pre-service teachers think in the context of quadrilaterals. It also contributes to our understanding of human thinking that is illustrated through the analysis of geometric discourse accompanied by vignettes.
In the 50 years since Mandelbrot identified the fractality of coastlines, mathematicians and physicists have developed a rich and beautiful theory describing the interplay between analytic, geometric and probabilistic aspects of the mathematics of fractals. Using classical and abstract analytic tools developed by Cantor, Hausdorff, and Sierpinski, they have sought to address fundamental questions: How can we measure the size of a fractal set? How do waves and heat travel on irregular structures? How are analysis, geometry and stochastic processes related in the absence of Euclidean smooth structure? What new physical phenomena arise in the fractal-like settings that are ubiquitous in nature?This book introduces background and recent progress on these problems, from both established leaders in the field and early career researchers. The book gives a broad introduction to several foundational techniques in fractal mathematics, while also introducing some specific new and significant results of interest to experts, such as that waves have infinite propagation speed on fractals. It contains sufficient introductory material that it can be read by new researchers or researchers from other areas who want to learn about fractal methods and results.
Geometry does not have to be confusing! Inside Mathematics: Geometry helps make sense of all of those lines and angles by showing its fascinating origins and how that knowledge is applied in everyday life. Written to engage and enthuse young minds, this accessible overview introduces readers to the amazing people who figured out how shapes work and how they can be used to build spaces and study places we cannot go, like the beginning of the Universe. Filled with enlightening illustrations and images, Geometry is arranged chronologically, from Euclid's revolution to the Poincare conjecture, to clearly show how ideas in mathematics evolved from the Ancient Egyptians in 3000 BC to the present day. What began as scratched circles and squares in the dirt has evolved into a branch of mathematics used to create realistic landscapes in video games, build mile-high skyscrapers, and manufacture robots so tiny they can swim in your bloodstream.
This book presents a selection of papers based on the XXXIII Bialowieza Workshop on Geometric Methods in Physics, 2014. The Bialowieza Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Bialowieza Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Bialowieza forest in eastern Poland.The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and mathematmtics.
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http://www.howtodothings.com/finance-real-estate/how-to-read-a-finance-chart
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math
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Investors and other members of the financial industry live and breathe finance charts. They can be concise ways to analyze and interpret data in a fully visual way. However, to anyone who is not an expert, these charts may seem like a confusing series of jagged lines.
It is actually quite easy to read a finance chart once you understand the information that goes into producing one.
First, you need to understand that a finance chart is usually measuring a single metric over a period of time. This is not always the case, but it is true most of the time. To graphically represent this data, we need to create a grid which allows us to plot where our metric is at any given moment.
The grid is broken up most simply into two areas. There is the vertical area and the horizontal area. Each of these is called an axis of the finance chart.
The horizontal axis (left-to-right) usually represents the time over which the metric will be measured on the chart. Placing things closer to the left of the finance chart will mean it happened earlier than things placed towards the right side of the chart.
The vertical axis (bottom-to-top) represents the value of the metric we are going to measure on the chart. Dots placed near the bottom of the finance chart represent lower numbers than those placed closer to the top.
All finance charts come with what are called keys, like a map key, which indicate what each of the axes represent. For a chart of stock values, for example, these could be showing months of the year horizontally and dollar value vertically. The key will also indicate the scale of the values used on the chart. Each horizontal inch could represent a month, a year, or ten years. It is very important to know the scale of measurement being used when reading a finance chart.
There are many different ways that the data can be graphically represented on a finance chart, but they are all really showing the same thing. If we know that in March a stock was worth $10, then we can draw an imaginary line from the place where March is located on the finance chart in the horizontal axis and stretch it up until it intersects an imaginary line drawn out from the vertical axis that represents $10. Where these two lines meet on the finance chart will create a point.
The points can be represented as simple dots, connected dots which will create the familiar zigzag lines often seen on most finance charts, or even as ascending solid bars representing each month.
However the data in the finance chart is represented, it is important to remember that it is really just an index into the grid created by the two axes. Follow the point down to find the date you want, and follow it right or left to find out the value at that time. This is how you read a simple finance chart.
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CC-MAIN-2016-44
| 2,783 | 10 |
https://books.google.com/books/about/Computational_methods_in_optimization_pr.html?id=B7zQAAAAMAAJ&hl=en
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math
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What people are saying - Write a review
We haven't found any reviews in the usual places.
The Case Where Control Constraints
E Examples for Continuous Systems
P An Example for a Continuous System
accessory minimum problem adjoint equations adjoint variables algorithm assume boundary conditions boundary value problem calculus of variations canonical systems equations CHAPTER Chemical CM CM CM H conjugate function conjugate gradient method control variable u(t convergence convex function convex set Cross-Current Extraction defined difference equation discrete systems dynamic programming evaluate example problems H CM H UJ Hamiltonian Hessian matrix I&EC Fundamentals inequality constraints Lapidus linear LJ LJ maximum principle maximum transform minimization mole/liter necessary conditions Newton-Raphson method nominal trajectory Nonlinear Programming nth stage numerical objective function obtained Optimal Control optimal solution optimal temperature profile optimization problems partial derivatives Pontryagin's maximum principle reaction reactor system recycle rO rO satisfied second-order gradient method supporting hyperplane terminal conditions terminal constraints Theory tubular reactor UJ H UJ UJ
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| 1,216 | 6 |
https://www.coursehero.com/tutors-problems/Economics/7822772-Choose-and-research-an-industry-where-there-has-been-a-pattern-of-chan/
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math
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(monopoly, oligopoly, etc.)and describe the industry and explain the general pattern of change of the particular market model.Then hypothesize the basic short-run and long-run behaviors of the model in the industry you have
chosen in a “market economy then analyze at least three (3) possible areas for the industry that could lead to transaction costs, and
explain each in detail.
Recently Asked Questions
- 7-2 Brookwood medical center case study 6 questions
- Phase shift circuit, with R=20 k, C=0.01 uF, R1=43 k. Determine the phase shift at: a) 500Hz b) 1 kHz c) 2 kHz The answer for this question are a) -2 tan^-2
- NMR analysis of product – state the chemical shift of the signals, splitting and integration. Assign the signals to the hydrogens responsible for the signal.
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https://nij.ojp.gov/library/publications/distance-analysis-i-and-ii-crimestat-iv-spatial-statistics-program-analysis
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math
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This is the third of three chapters on "Spatial Descriptions" from the user manual for CrimeStat IV, a spatial statistics package that can analyze crime incident location data.
The chapter, "Distance Analysis I and II," describes the characteristics of the distances between points. The chapter focuses on "second-order" properties of distance analysis, which refers to sub-regional or "neighborhood" crime patterns within the overall distribution. Second-order characteristics show how particular crime incidents are concentrated in particular environments. The chapter has two sections on distance analysis. In Distance Analysis I, various second-order statistics are provided; and in Distance Analysis II, four routines for calculating and outputting distance matrices are discussed. Issues related to Distance Analysis I pertain to the nearest neighbor index, the K-order nearest neighbor, the linear nearest neighbor index, the linear K-order nearest neighbor index, and Ripley's "K" statistic. Assigning primary points to secondary points is also discussed under Distance Analysis I. Extensive figures display computer screens, and attachments discuss SARS (Severe Acute Respiratory Syndrome) and the distribution of passengers on an airplane; nearest neighbor analysis for "man with a gun" calls in Charlotte, NC, in 1989; and "K Function Analysis to Determine Clustering in the 'police confrontations' dataset in Buenos Aires Province, Argentina in 1989." 12 references
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https://www.hindawi.com/journals/jps/2009/873274/
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math
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Research Article | Open Access
Tien-Chung Hu, Neville C. Weber, "A Note on Strong Convergence of Sums of Dependent Random Variables", Journal of Probability and Statistics, vol. 2009, Article ID 873274, 7 pages, 2009. https://doi.org/10.1155/2009/873274
A Note on Strong Convergence of Sums of Dependent Random Variables
For a sequence of dependent square-integrable random variables and a sequence of positive constants , conditions are provided under which the series converges almost surely as . These conditions are weaker than those provided by Hu et al. (2008).
1. Introduction and Results
Let be a sequence of square-integrable random variables defined on a probability space and let be a sequence of positive constants. The random variables are not assumed to be independent. Past research has focussed on conditions that ensure the strong convergence of two distinct but related series: If the second sequence converges to 0 almost surely, then is said to obey the strong law of large numbers (SLLN).
Assume that there exists a sequence of constants such that Our interest is in conditions on the growth rates of , , and which imply strong convergence of the above series.
There is an extensive literature on strong laws for independent random variables. Strong laws have been derived for various dependence structures such as negative association (e.g., Kuczmaszewska ), quasi-stationarity (e.g., Móricz , Chobanyan et al. ), and orthogonality (e.g., Stout ).
Hu et al. focus on the strong convergence of the series without imposing strong conditions on the nature of the variances and covariances. Our aim is to weaken their condition on the covariances and establish the following theorem.
Theorem 1.1. Let be a sequence of square-integrable random variables and suppose that there exists a sequence of constants such that (1.2) holds. Let be a sequence of positive constants. Assume that there exists a constant such that, for all , Suppose that Then
To motivate the general nature of our result consider the following example. Let be a sequence of zero mean random variables where where is a stationary time series with autocovariance function and is a sequence of independent, zero mean random variables distributed independently of . Let Var Thus what we observe is an underlying stationary series disturbed by a noise process with variance that can depend on
We have Var and Cov, Condition (3.1) in Theorem of Hu et al. , which is the same as (1.4), is a constraint on the values whereas their condition (3.2) is a constraint on . In Chapter 2 of Stout the condition on the variances is shown to be close to optimal for sequences of orthogonal random variables. Lyons provides an SLLN for random variables with bounded variances under the condition One might conjecture that the condition (1.8) could be relaxed to The above theorem, whilst allowing for far more general models than (1.7), moves us closer to this constraint on the values.
For long range dependent stationary processes we have where and is a slowly varying function. Theorem 1.1 enables the strong convergence result to be extended to processes where the correlation decays at a slower rate than for
Applying Kronecker's lemma the strong law of large numbers result is an immediate consequence of the above theorem.
Corollary 1.2. Under the conditions of Theorem 1.1, if is monotone increasing, the strong law of large numbers holds, that is,
There are strong law results under weaker conditions than (1.5) but with stronger conditions on the variance (see, e.g., Lyons , Chobanyan et al. ). Both papers show that if the summands have bounded variance, then (1.5) can be weakened to Our approach focusses on the convergence of the series in (1.6) and relies on Kronecker's Lemma to obtain the strong law. If the aim is purely to obtain the SLLN, then alternative conditions might be possible as it is possible to construct sequences and such that but diverges. For example, take and Thus we can have the strong law holding but the series in (1.6) diverging.
Throughout this paper, the symbol denotes a generic constant which is not necessarily the same at each appearance. We first prove a number of lemmas that enable us to obtain tighter bounds for key expressions in the proof of Theorem of Hu et al. .
Proof. For all , ,
Lemma 2.2. For ,
Proof. Note that is an increasing function for Thus, for , Hence for ,
Lemma 2.3. For define Then , and, in general,
Proof. The result for is the sum of a standard geometric progression. The general result follows by noting Thus
Proof of Theorem 1.1. We will follow the method of proof in Theorem in Hu et al. . To prove (1.6) we first show that is a Cauchy sequence for convergence in which will imply convergence in probability. Using Lemmas 2.1 and 2.2,
Therefore there exists a random variable such that
Next we will show that a.s. Let be arbitrary. Note where the last line follows by using (1.4) and (1.5). Thus by the Borel Cantelli lemma almost surely. To finish the proof we utilize the generalization of the Rademacher-Menchoff maximal inequality given by Serfling and argue as in Hu et al. . It is sufficient to show that, for any , Using Serfling's inequality and (3.8) from Hu et al.
- A. Kuczmaszewska, “The strong law of large numbers for dependent random variables,” Statistics & Probability Letters, vol. 73, no. 3, pp. 305–314, 2005.
- F. Móricz, “The strong laws of large numbers for quasi-stationary sequences,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 38, no. 3, pp. 223–236, 1977.
- S. Chobanyan, S. Levental, and H. Salehi, “Strong law of large numbers under a general moment condition,” Electronic Communications in Probability, vol. 10, pp. 218–222, 2005.
- W. F. Stout, Almost Sure Convergence, Academic Press, New York, NY, USA, 1974.
- T.-C. Hu, A. Rosalsky, and A. I. Volodin, “On convergence properties of sums of dependent random variables under second moment and covariance restrictions,” Statistics & Probability Letters, vol. 78, no. 14, pp. 1999–2005, 2008.
- R. Lyons, “Strong laws of large numbers for weakly correlated random variables,” The Michigan Mathematical Journal, vol. 35, no. 3, pp. 353–359, 1988.
- R. J. Serfling, “Moment inequalities for the maximum cumulative sum,” Annals of Mathematical Statistics, vol. 41, pp. 1227–1234, 1970.
Copyright © 2009 Tien-Chung Hu and Neville C. Weber. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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CC-MAIN-2022-33
| 6,651 | 33 |
https://engagedscholarship.csuohio.edu/sciphysics_facpub/302/
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math
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Phase Transition and Surface Sublimation of A Mobile Potts Model
Physical Review E
We study in this paper the phase transition in a mobile Potts model by the use of Monte Carlo simulation. The mobile Potts model is related to a diluted Potts model which is also studied here by a mean-field approximation. We consider a lattice where each site is either vacant or occupied by a q-state Potts spin. The Potts spin can move from one site to a nearby vacant site. In order to study the surface sublimation, we consider a system of Potts spins contained in a recipient with a concentration c defined as the ratio of the number of Potts spins Ns to the total number of lattice sites NL=Nx×Ny×Nz. Taking into account the attractive interaction between the nearest-neighboring Potts spins, we study the phase transition as functions of various physical parameters such as the temperature, the shape of the recipient and the spin concentration. We show that as the temperature increases, surface spins are detached from the solid phase to form a gas in the empty space. Surface order parameters indicate different behaviors depending on the distance to the surface. At high temperatures, if the concentration is high enough, the interior spins undergo a first-order phase transition to an orientationally disordered phase. The mean-field results are shown as functions of temperature, pressure and chemical potential, which confirm in particular the first-order character of the transition.
Reyre, A. Bailly; Diep, H. T.; and Kaufman, Miron, "Phase Transition and Surface Sublimation of A Mobile Potts Model" (2015). Physics Faculty Publications. 302.
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http://bigchance.biz/roulette-unique-numbers.php
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Please re-read carefuly, this time you might count correctly and find that both of the sequences are 10 results length. Below is a typical progression table for a spin sequence where 20 unique numbers have come out in 34 consecutive spins e.
Its all about how random numbers work. Where will that happen? That's what makes it so powerful. However, these are only the most basic of roulette odds.
We are trying this out because we are not only very confident that our System works, but that it is simple enough for everyone to use, and if we can have an army of users winning with our System, then we will earn a lot more money than simply using it ourselves, while at the same time giving more people an opportunity to use our System.
So Hon dah casino robbery got out my trusty Excel sheet and set to work. Feel free to double-check this by manually calculating the Probability of Success, Expected Return, Progression, and Bankroll Required based on the spins entered.
It all depends where you jump into the wave and if that wave of luck is on its way up or on its way down. At a choppy table, where wins and losses alternate and balance out, you would have lost 15 units after 30 decisions and things would be pretty boring.
Winning Roulette Odds
But just how often does a number have to be hit in order for players to be able to bet on it profitably? This bet pays Before the Trigger Spin Before a Bet signal was triggered, there were 5 spins left in the sequence and only 20 unique numbers had shown.
I produce blocks of 10 numbers random numbers and showed where 7 from 8 had happened, and where the 9th was a repeat, and where the 10th was also a repeat i. There would be no need to because they would already be loaded! That makes the calculation: This system is desi The Probability of Success with this example is the proportional probability of the favorable scenarios with 21, 22, or 23 unique numbers divided by the proportional probability of all scenarios with 20, 21, 22, or 23 unique numbers confer above: Using this Average Profit, we can calculate the Expected Return: So 9 unique numbers with 1 repeat looks like this: You are forgetting something!
Roulette Payouts and Odds
There are no doubles. Click on the images to enlarge them and focus on the small details of the program in order to fully appreciate what is happening.
Since the Probabilities of Success given are not some random made-up number, but a mathematically-derived probability based on actual outcomes in million simulations of spin sequences we've confirmed this in our teststhe player knows precisely what chance they have of being successful on any given bet signal.
Another example to show how useless those mainstream gambling math theories are is that first they claim that all EC's red,black,odd,even,high,low have equal odds and then the very same math "gurus" claim that this sequence: You get to stand on the trapdoor blind to when it will open. Not only that, but in 37 spins, 23 and 24 unique numbers are most likely to appear each about once every 5 sequences.
Notice how in those 10 million simulations, there was never less than 14 or more than 33 unique numbers. I make my living out of gambling, I've invented what you call the Holy Grail of gambling. That is true at least for standard roulette games that pay out at odds that would be fair if the wheel only contained the 36 numbers without zeroes. At the most basic level, we talk about roulette odds in terms of the house edge — the advantage the casino holds over the player.
Progression table for a spin sequence with 20 unique numbers after 34 spins. Furthermore, with this information, we can give you one simple winning system: Think of each ascending number in this series as a rung of a ladder: In relation to Roulette, he shows that if you spin 10 numbers, or more mathematically speaking, if we run 10 consecutive random numbers, there are odds that some or all the numbers will be unique.
If they don't alternate or balance, you might have your bets on the losing side, and that would be worse. Again, that is where the Proportional-Probabilities System comes in as it takes into account the shifting proportional-probabilities mid-sequence which exploit the table of probabilities above and leads to several favorable scenarios.
Below is a screenshot of the PP system in action.
Luck waves up and down. In order to do so safely, the rungs must not be too far apart.
That is 2, 3, 17, 1, 24, 33, 34, 29, 11, In addition, when we win we win 35 units, but when we lose we only lose one unit. These are roulette wheels that do not have the proper construction to ensure that every pocket will be hit with equal probability.
Can you start right away? How much experience do you have with Roulette:
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| 4,764 | 19 |
http://crapsforum.com/threads/my-odds-problem.12448/
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math
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Remember, this is the Beginner Zone, so no wising off, please. I'm math challenged, and craps has exposed me to more math than I can understand. One of those things is odds, which apply to all gambling. I do understand the odds of certain numbers showing compared to the 7: The 6 & 8, for example will show 5 times out of 36; the 7 will show 6 times, giving odds of 5:6. For payout (I think), the ratio is reversed, 6:5 for true odds. And so forth re: rest of the numbers. I get that. Where I get hung up is when I see odds like these in today's LV Review-Journal sports page: Odds To Win World Series: Chicago Cubs 9-2 SF Giants 8-1 So, 9-2 odds are better than 8-1? And I suppose these are payout odds, so the actual odds are expressed as 2-9 & 1-8? But, why is 2-9 better than 1-8? I thought the lower the numbers, the better the odds. I get that these (& all) odds can be expressed as fractions: 2/9, 1/8, but I still don't get that. Another example: Odds To Win NBA Title: Golden State 1-2 SA Spurs 19-5 Now if GS's odds are payout odds, you bet $2 to win $1? Sounds like don't craps wagers, to me. And, what's w/ SA at 19-5? How does an oddsmaker determine 19-5 odds? Actual odds would be 2-1 & 5-19. But it becomes ridiculous to have 2/1, I think. 5/19 as a fraction is ok, but I don't get the 5-19 number. How does an oddsmaker determine that? 777 has a chapter on odds in his book, which I have, but it's all packed up, waiting for my next move. Would appreciate anyone willing to explain all this to a math dummy.
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https://www.abebooks.co.uk/9780070578203/Elementary-Numerical-Computing-Mathematica-Mcgraw-Hill-0070578206/plp
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math
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A practical introduction to numerical methods at an elementary level. It exposes students to a range of possibilities to scientific computing. Although oriented towards Mathematica, the book can be used with other programming languages. It contains lessons on Mathematica but also assumes reasonable access to the Mathematica manual. Avoiding partial derivatives which many students study but fail to master, it covers systems of ordinary differential equations to give the student an accurate picture of scientific computing. The main purpose of the book is to teach the principles of numerical analysis. In addition, it sets out to teach some simple and useful numerical methods; to indicate the sort of techniques that are used in actual numerical software and thereby suggest what kind of performance migh be expected; to give practical advice on the assessment and enhancement of accuracy; and to show how problems requiring numerical computation arise in application. Also available is an instructor's manual (0-07-057821-4).
"synopsis" may belong to another edition of this title.
Book Description Mcgraw-Hill College, 1993. Hardcover. Book Condition: New. Bookseller Inventory # DADAX0070578206
Book Description Mcgraw-Hill College, 1993. Hardcover. Book Condition: New. book. Bookseller Inventory # 0070578206
Book Description Mcgraw-Hill College, 1993. Hardcover. Book Condition: New. Bookseller Inventory # P110070578206
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| 1,431 | 5 |
https://ymsc.tsinghua.edu.cn/en/info/1050/2846.htm
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math
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Speaker：Ian Gleason (Bonn University）
Schedule：10:00-11:30 am, March 13, 14, 15, 2024
Venue：B627, Shuangqing Complex Building A; Zoom Meeting ID: 4552601552 Passcode: YMSC
Spatial diamonds were introduced by Scholze to give geometric structure to naturally arising moduli spaces in p-adic Hodge theory. The theory of diamonds can be thought of as a generalization of the theory of rigid spaces. Scholze further proposes the category of v-sheaves as a mean to study spaces of non-analytic nature. Kimberlites are v-sheaves subject to some axioms that capture the key behavior of formal schemes. In this minicourse we discuss the definition of a spatial kimberlite and discuss some key properties that kimberlites have.
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| 725 | 4 |
https://uwspace.uwaterloo.ca/handle/10012/6824
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math
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Towards Theoretical Foundations of Clustering
MetadataShow full item record
Clustering is a central unsupervised learning task with a wide variety of applications. Unlike in supervised learning, different clustering algorithms may yield dramatically different outputs for the same input sets. As such, the choice of algorithm is crucial. When selecting a clustering algorithm, users tend to focus on cost-related considerations, such as running times, software purchasing costs, etc. Yet differences concerning the output of the algorithms are a more primal consideration. We propose an approach for selecting clustering algorithms based on differences in their input-output behaviour. This approach relies on identifying significant properties of clustering algorithms and classifying algorithms based on the properties that they satisfy. We begin with Kleinberg's impossibility result, which relies on concise abstract properties that are well-suited for our approach. Kleinberg showed that three specific properties cannot be satisfied by the same algorithm. We illustrate that the impossibility result is a consequence of the formalism used, proving that these properties can be formulated without leading to inconsistency in the context of clustering quality measures or algorithms whose input requires the number of clusters. Combining Kleinberg's properties with newly proposed ones, we provide an extensive property-base classification of common clustering paradigms. We use some of these properties to provide a novel characterization of the class of linkage-based algorithms. That is, we distil a small set of properties that uniquely identify this family of algorithms. Lastly, we investigate how the output of algorithms is affected by the addition of small, potentially adversarial, sets of points. We prove that given clusterable input, the output of $k$-means is robust to the addition of a small number of data points. On the other hand, clusterings produced by many well-known methods, including linkage-based techniques, can be changed radically by adding a small number of elements.
Cite this version of the work
Margareta Ackerman (2012). Towards Theoretical Foundations of Clustering. UWSpace. http://hdl.handle.net/10012/6824
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| 2,247 | 5 |
https://essaycomplex.com/blood-protoplasm-normal-distribution/
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Medical: Blood Protoplasm – Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variablethat represents the number of milligrams of porphyrin per deciliter of blood. In healthy adults x is approximately normally distributed with the meanμ= 38 and standard deviationσ = 12. What is the probabilitythat:
(a) x is less than 60
(b) x is greater than 16
(c) x is between 16 and 60
(d) x is more than 60 (this may indicate infection, anemia, or another type of illness).
M = 38, s = 12; z = (x – M)/s
(a) z = (60 – 38)/12 = 1.833
P(x < 60) = Area under the Standard Normal Curve to the …
The required probabilities have been worked out by calculating the z- scores. Neat work.
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| 759 | 9 |
https://projecteuclid.org/journals/algebraic-and-geometric-topology/volume-20/issue-6/Small-C1-actions-of-semidirect-products-on-compact-manifolds/10.2140/agt.2020.20.3183.short
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math
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Let be a compact fibered –manifold, presented as a mapping torus of a compact, orientable surface with monodromy , and let be a compact Riemannian manifold. Our main result is that if the induced action on has no eigenvalues on the unit circle, then there exists a neighborhood of the trivial action in the space of actions of on such that any action in is abelian. We will prove that the same result holds in the generality of an infinite cyclic extension of an arbitrary finitely generated group provided that the conjugation action of the cyclic group on has no eigenvalues of modulus one. We thus generalize a result of A McCarthy, which addressed the case of abelian-by-cyclic groups acting on compact manifolds.
"Small $C^1$ actions of semidirect products on compact manifolds." Algebr. Geom. Topol. 20 (6) 3183 - 3203, 2020. https://doi.org/10.2140/agt.2020.20.3183
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CC-MAIN-2021-31
| 874 | 2 |
https://www.tragaluzeditores.com/lies-youve-been-told-about-what-does-exp-mean-math/
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math
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You are also able to get a step-by-step tutorial from here. Teacher will have the ability to differentiate student learning by making the problems more difficult to challenge increased level students. paramount essays If you google Blend Modes in Photoshop you’re likely to obtain plenty of technical tutorials that might be tough to comprehend.
For samples, if it’s known they are drawn from a symmetric unimodal distribution, the sample mean can function as an estimate of the populace mode. To locate the median, your numbers need to be listed in numerical order from smallest to largest, and that means you might need to rewrite your list before it’s possible to discover the median. If there’s a finite number of elements, the median is no problem to find.
Mean is the average of each of the numbers. Hence, it is the value in the middle position. It is only unique if the sample size is odd.
It is sometimes called the average. Hence, it is the value in the middle position. It is more useful when the value variance is not important.
It is sometimes called the average. It is basically the average number. It is only unique if the sample size is odd.
The 30-Second Trick for What Does Exp Mean Math
Fantastic simplification will enable the economists to concentrate just on the most relevant variables. Poisson regression has a lot of extensions useful for count models. There are some other dimensions whom I think equations differ in important ways.
It can be difficult to work out, as it’s the number found in the center of the set when they’re listed in numerical order! The number e is a famed irrational number, and is among the most significant https://pritzker.uchicago.edu/page/admissions numbers in mathematics. The 2 middle numbers only will need to get averaged while the data set has an even number of information points in it.
By the moment you finish reading this short article, you ought to have a clearer idea of the way to use blend modes and where to start your experimentation, which then should lower the time that it takes to attain the outcomes you’re searching for. In fact, all people today act differently. The smaller the slice you give to every individual, the more people you’ll be able to feed.
Since 98 isn’t a wonderful neat power of 10 (the manner that 100 was), I cannot be clever with exponents to get there at a specific answer. The division by 2 comes from the simple fact a parallelogram can be broken into 2 triangles. This solution won’t return an answer once the angles cancel out to a very small magnitude.
The mid-range is a kind of mean, while the interquartile range is talking about a chunk of information in the midst of a data collection. Adding this text doesn’t have any influence on the behaviour of the program, but nevertheless, it can be helpful for every time an individual wants to read and understand the code at a subsequent date. It’s assumed that you understand how to enter data or read data files that is covered in the very first chapter, and you know about the fundamental data types.
The Basics of What Does Exp Mean Math
The intention of this course is to supply a thorough summary of the skills needed to navigate the mathematical demands of contemporary life and prepare students for a deeper knowledge of information presented in mathematical terms. The mode is easily the most frequent member of the group. Locate the mean of these distribution.
They have some significantly different properties which are best left for a different discussion. These sections contain additional information about the mgf. Let’s compare the outcomes of the previous two examples.
Facts, Fiction and What Does Exp Mean Math
A set of information can be bimodal. Through the usage of the scientific method, economists can break down complex financial scenarios so as to obtain a deeper knowledge of critical data. Observation of information is important for economists since they take the outcome and interpret them in a meaningful way.
If You Read Nothing Else Today, Read This Report on What Does Exp Mean Math
So bear that in mind as you’re doing problems also keep this in mind if you’re go into advertising you might opted to advertise the normal salary rather than the median salary if you’ve got an outlier data that type of warps your data set. Because of this, it’s important that economists can break down and study complex info. As an example, positive financial theory would describe how money supply development impacts inflation, but it doesn’t offer any guidance on what policy ought to be paper proofreading service followed.
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This post will discuss a process to locate the probability distribution which best fits your specified state of knowledge. Calculus is commonly used in economics and has the capability to address many troubles that algebra cannot. It can have a very long time to debug such errors.
It has average of 2, three or four numbers with different difficulty levels. To try to remember the definition of a median, just consider the median of a road, that’s the middlemost area of the road. The period median refers to a typical value indicated by the center number or numbers in a sequence.
Within this section you are going to be requested to learn more about the functionality of your scientific calculator, and to utilize your calculator to address some simple issues. Unary minus If the very first character is a minus, the calculator will assume you wish to subtract from the prior result. Most calculators will tell you you can’t divide by zero.
First create a function The very first step is to produce a function. The mode is just the particular value that occurs most frequently. When seeking the mode, there may be more than 1 mode or no mode.
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https://www.hackmath.net/en/math-problem/2262
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math
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Diagonals in diamond
In the rhombus is given a = 160 cm, alpha = 60 degrees. Calculate the length of the diagonals.
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AC= 40cm , angle DAB=38 , angle DCB=58 , angle DBC=90 , DB is perpendicular on AC , find BD and AD
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https://classroomsecrets.co.uk/year-6-calculating-ratio-lesson-slides/
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math
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Year 6 Calculating Ratio Lesson Slides
These Year 6 Calculating Ratio Lesson Slides are designed to support your teaching of this objective. The slides are accompanied by a teacher explanation and have interactive questions embedded within to check understanding.
National Curriculum Objectives
Mathematics Year 6: (6R3) Solve problems involving similar shapes where the scale factor is known or can be found
Mathematics Year 6: (6R4) Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
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https://journalofinequalitiesandapplications.springeropen.com/articles/10.1155/2009/868423
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math
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- Research Article
- Open Access
Quadratic-Quartic Functional Equations in RN-Spaces
© M. Eshaghi Gordji et al. 2009
- Received: 20 July 2009
- Accepted: 3 November 2009
- Published: 1 December 2009
We obtain the general solution and the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary -norms .
- Banach Space
- Vector Space
- General Solution
- Abelian Group
- Functional Equation
The stability problem of functional equations originated from a question of Ulam in concerning the stability of group homomorphisms. Let be a group and let be a metric group with the metric Given , does there exist a such that if a mapping satisfies the inequality for all , then there exists a homomorphism with for all In other words, under what condition does there exists a homomorphism near an approximate homomorphism? The concept of stability for functional equation arises when we replace the functional equation by an inequality which acts as a perturbation of the equation. Hyers gave a first affirmative answer to the question of Ulam for Banach spaces. Let be a mapping between Banach spaces such that
for all and some Then there exists a unique additive mapping such that
for all Moreover, if is continuous in for each fixed then is -linear. In 1978, Rassias provided a generalization of Hyers' theorem which allows the Cauchy difference to be unbounded. In Gajda answered the question for the case , which was raised by Rassias. This new concept is known as Hyers-Ulam-Rassias stability of functional equations (see [5–12]). The functional equation
is related to a symmetric biadditive mapping. It is natural that this equation is called a quadratic functional equation. In particular, every solution of the quadratic functional equation (1.3) is said to be a quadratic mapping. It is well known that a mapping between real vector spaces is quadratic if and only if there exits a unique symmetric biadditive mapping such that for all (see [5, 13]). The biadditive mapping is given by
The Hyers-Ulam-Rassias stability problem for the quadratic functional equation (1.3) was proved by Skof for mappings , where is a normed space and is a Banach space (see ). Cholewa noticed that the theorem of Skof is still true if relevant domain is replaced an abelian group. In , Czerwik proved the Hyers-Ulam-Rassias stability of the functional equation (1.3). Grabiec has generalized the results mentioned above.
In , Park and Bae considered the following quartic functional equation
In fact, they proved that a mapping between two real vector spaces and is a solution of (1.5) if and only if there exists a unique symmetric multiadditive mapping such that for all . It is easy to show that the function satisfies the functional equation (1.5), which is called a quartic functional equation (see also ). In addition, Kim has obtained the Hyers-Ulam-Rassias stability for a mixed type of quartic and quadratic functional equation.
The Hyers-Ulam-Rassias stability of different functional equations in random normed and fuzzy normed spaces has been recently studied in [21–26]. It should be noticed that in all these papers the triangle inequality is expressed by using the strongest triangular norm .
The aim of this paper is to investigate the stability of the additive-quadratic functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary continuous -norms.
In this sequel, we adopt the usual terminology, notations, and conventions of the theory of random normed spaces, as in [22, 23, 27–29]. Throughout this paper, is the space of distribution functions, that is, the space of all mappings such that is left-continuous and nondecreasing on and . Also, is a subset of consisting of all functions for which , where denotes the left limit of the function at the point , that is, . The space is partially ordered by the usual point-wise ordering of functions, that is, if and only if for all in . The maximal element for in this order is the distribution function given by
Definition 1.1 (see ).
A mapping is a continuous triangular norm (briefly, a continuous -norm) if satisfies the following conditions:
(a) is commutative and associative;
(b) is continuous;
(c) for all ;
(d) whenever and for all .
Typical examples of continuous -norms are , and (the Lukasiewicz -norm). Recall (see [30, 31]) that if is a -norm and is a given sequence of numbers in , then is defined recurrently by and for . is defined as It is known that for the Lukasiewicz -norm, the following implication holds:
Definition 1.2 (see ).
A random normed space (briefly, RN-space) is a triple , where is a vector space, is a continuous -norm, and is a mapping from into such that the following conditions hold:
(RN1) for all if and only if ;
(RN2) for all , ;
(RN3) for all and
for all and is the minimum -norm. This space is called the induced random normed space.
Let be an RN-space.
A sequence in is said to be convergent to in if, for every and , there exists a positive integer such that whenever .
A sequence in is called a Cauchy sequence if, for every and , there exists a positive integer such that whenever .
An RN-space is said to be complete if and only if every Cauchy sequence in is convergent to a point in .
Theorem 1.4 (see ).
If is an RN-space and is a sequence such that , then almost everywhere.
In this paper, we deal with the following functional equation:
on RN-spaces. It is easy to see that the function is a solution of (1.9).
In Section 2, we investigate the general solution of the functional equation (1.9) when is a mapping between vector spaces and in Section 3, we establish the stability of the functional equation (1.9) in RN-spaces.
We need the following lemma for solution of (1.9). Throughout this section, and are vector spaces.
If a mapping satisfies (1.9) for all then is quadratic-quartic.
We show that the mappings defined by and defined by are quadratic and quartic, respectively.
Letting in (1.9), we have . Putting in (1.9), we get . Thus the mapping is even. Replacing by in (1.9), we get
for all . Therefore, the mapping is quadratic.
To prove that is quartic, we have to show that
for all .
Therefore, the mapping is quartic. This completes the proof of the lemma.
for all .
for all The proof of the converse is obvious.
Throughout this section, assume that is a real linear space and is a complete RN-space.
for all and all
Since the right-hand side of the inequality (3.17) tends to as and tend to infinity, the sequence is a Cauchy sequence. Thus we may define for all .
Now we show that is a quadratic mapping. Replacing with and in (3.1), respectively, we get
Taking the limit as , we find that satisfies (1.9) for all . By Lemma 2.1, the mapping is quadratic.
Letting the limit as in (3.16), we get (3.3) by (3.10).
Finally, to prove the uniqueness of the quadratic mapping subject to (3.3), let us assume that there exists another quadratic mapping which satisfies (3.3). Since for all and all from (3.3), it follows that
for all and all . Letting in (3.19), we conclude that , as desired.
for all and all
Since the right-hand side of (3.36) tends to as and tend to infinity, the sequence is a Cauchy sequence. Thus we may define for all .
Now we show that is a quartic mapping. Replacing with and in (3.20), respectively, we get
Taking the limit as , we find that satisfies (1.9) for all . By Lemma 2.1 we get that the mapping is quartic.
Letting the limit as in (3.35), we get (3.22) by (3.29).
Finally, to prove the uniqueness of the quartic mapping subject to let us assume that there exists a quartic mapping which satisfies (3.22). Since and for all and all from (3.22), it follows that
for all and all . Letting in (3.38), we get that , as desired.
for all and all
for all and all . Hence we obtain (3.41) by letting and for all The uniqueness property of and is trivial.
C. Park was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2009-0070788).
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https://www.oceanicpharmachem.com/product-detail/15/13
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math
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API Product : Carvedilol Phosphate
CEP : -
WCC : ?
Therapeutic Use : Cardiac therapy; Beta-blocking agents; Antihypertensives
Cardiac therapy; Beta-blocking agents; Antihypertensives
Originator : GlaxoSmithKline
CAS No. : 610309-89-2
Trade Name. : Coreg
Molecular Weight : 522.491 g/mol
Molecular Formula : C24H31N2O9P
Carvedilol is used to treat high blood pressure and heart failure. It is also used after a heart attack to improve the chance of survival if your heart is not pumping well. Lowering high blood pressure helps prevent strokes, heart attacks, and kidney problems.
Carvedilol, sold under the brand name Coreg among others, is a medication used to treat high blood pressure, congestive heart failure (CHF), and left ventricular dysfunction in people who are otherwise stable. For high blood pressure, it is generally a second-line treatment. It is taken by mouth. Common side effects include dizziness, tiredness, joint pain, low blood pressure, nausea, and shortness of breath. Severe side effects may include bronchospasm. Safety during pregnancy or breastfeeding is unclear. Use is not recommended with liver problems. Carvedilol is a nonselective beta blocker and alpha-1 blocker. How it improves outcomes is not entirely clear but may involve dilation of blood vessels.
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https://www.physicsforums.com/threads/resultant-force.346183/
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math
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1. The problem statement, all variables and given/known data An object is at the origin. They're four perpendicular forces acting upon it. In the negative x axis, 18 N. positive x axis, 10 N. negative y axis, 8 N. and positive y axis 15 N. calculate the resultant force. What angle is it at? 2. Relevant equations F=Ma? 3. The attempt at a solution Not really sure how to get the resultant force. Do you just add 8+10-15-18? (since 15 and 18 are negative)? For the angle, would it be 90 degrees?
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CC-MAIN-2018-13
| 495 | 1 |
https://brandzkit.com/tag/what-is-the-mass-m-of-the-fish/
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math
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Ignoring the mass of the spring, what is the mass m of the fish?
What is the mass of the fish? You can ignore the mass of the spring.? The scale of a spring balance reading from zero to 200 N is 12.5 cm long. A fish hanging from the bottom of the spring oscillates vertically at 2.60 Hz. __________________________________ Force constant=200/0.125=1600 N/m Frequency= f =(1/2pi) sq rt [k/m] … Read more
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http://www.abuildersengineer.com/2012/12/load-transfer-mechanism-drilled-pier.html
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math
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If the pier is instrumented, the load distribution along the pier can be determined at different stages of loading.
Typical load distribution curves plotted along a pier are shown in Fig 17.10(b) (O'Neill and Reese, 1999).
These load distribution curves are similar to the one shown in Fig. 15.5(b). Since the load transfer mechanism for a pier is the same as that for a pile, no further discussion on this is necessary here. However, it is necessary to study in this context the effect of settlement on the mobilization of side shear and base resistance of a pier. As may be seen from Fig. 17.11, the maximum values of base and side resistance are not mobilized at the same value of displacement. In some soils, and especially in some brittle rocks, the side shear may develop fully at a small value of displacement and then decrease with further displacement while the base resistance is still being mobilized (O'Neill and Reese, 1999). If the value of the side resistance at point A is added to the value of the base resistance at point B, the total resistance shown at level D is overpredicted. On the other hand, if the designer wants to take advantage primarily of the base resistance, the side resistance at point C should be added to the base resistance at point B to evaluate Qu. Otherwise, the designer may wish to design for the side resistance at point A and disregard the base resistance entirely.
Figure 17.10 Typical set of load distribution curves (O'Neill and Reese, 1999)
Figure 17.11 Condition in which (Qb + Qf) is not equal to actual ultimate resistance
Figure 15.5 (b) general shear failure in the strong lower soil
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| 1,637 | 6 |
https://www.freelancer.com/projects/Video-Services-Social-Networking/youtube-likes/
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math
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Need real likes, views and comments for my videos each = 1000
both videos are under the same account on youtube.
19 freelancers are bidding on average ₹4470 for this job
Hallo sir, We only say what we can do, we can not say which we can not do cos we work for our client satisfation. $$$$$$Check PMB for details$$$$$$
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https://www.esaga.uni-due.de/jochen.heinloth/ss17/oberseminar/maslovaric/
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math
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Abstract Marcel Maslovaric
GIT and Mori dream spaces
Abstract: When forming a quotient via Geometric Invariant Theory (GIT) we need to specify a notion of stability. Different choices of stability give different quotients, which are related by rational maps.
In this talk I want to explain how the space of stability notions is related to the birational geometry of the quotients. This will incorporate the space of line bundles on the quotients and the various cones therein (nef, effective, moving).
More concretely, I will focus on the case of a Mori dream space, where this interplay works very well.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474581.68/warc/CC-MAIN-20240225035809-20240225065809-00447.warc.gz
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http://moodle.dave-wood.org/
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math
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Content: How do you reconstruct a curve given its slope at every point? Can you predict the trajectory of a tennis ball? The basic theory of ordinary differential equations (ODEs) as covered in this module is the cornerstone of all applied mathematics. Indeed, modern applied mathematics essentially began when Newton developed the calculus in order to solve (and to state precisely) the differential equations that followed from his laws of motion.
However, this theory is not only of interest to the applied mathematician: indeed, it is an integral part of any rigorous mathematical training, and is developed here in a systematic way. Just as a `pure' subject like group theory can be part of the daily armoury of the `applied' mathematician , so ideas from the theory of ODEs prove invaluable in various branches of pure mathematics, such as geometry and topology.
In this module we will cover relatively simple examples, first order equations
linear second order equations
and coupled first order linear systems with constant coefficients, for most of which we can find an explicit solution. However, even when we can write the solution down it is important to understand what the solution means, i.e. its `qualitative' properties. This approach is invaluable for equations for which we cannot find an explicit solution.
We also show how the techniques we learned for second order differential equations have natural analogues that can be used to solve difference equations.
The course looks at solutions to differential equations in the cases where we are concerned with one- and two-dimensional systems, where the increase in complexity will be followed during the lectures. At the end of the module, in preparation for more advanced modules in this subject, we will discuss why in three-dimensions we see new phenomena, and have a first glimpse of chaotic solutions.
Aims: To introduce simple differential and difference equations and methods for their solution, to illustrate the importance of a qualitative understanding of these solutions and to understand the techniques of phase-plane analysis.
Objectives: You should be able to solve various simple differential equations (first order, linear second order and coupled systems of first order equations) and to interpret their qualitative behaviour; and to do the same for simple difference equations.
The primary text will be:
J. C. Robinson An Introduction to Ordinary Differential Equations, Cambridge University Press 2003.
Additional references are:
W. Boyce and R. Di Prima, Elementary Differential Equations and Boundary Value Problems, Wiley 1997.
C. H. Edwards and D. E. Penney, Differential Equations and Boundary Value Problems, Prentice Hall 2000.
K. R. Nagle, E. Saff, and D. A. Snider, Fundamentals of Differential Equations and Boundary Value Problems, Addison Wesley 1999.
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https://community.livejournal.com/icons-/123812.html
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math
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since a lot of ppl asked me to do it.
I created a community for my graphics, before i was posting them at my locked journal.
To start i created a graphics archive entry, with 302 icons.
# 140 movies, misc celebs etc..
# 54 text icons
# 108 stock icons
you can find all of them, HERE @ zone36
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https://asep.lib.cas.cz/arl-cav/cs/detail-cav_un_epca-0488780-Descartes-on-the-Unification-of-Arithmetic-Algebra-and-Geometry-Via-the-Theory-of-Proportions/
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Počet záznamů: 1
Descartes on the Unification of Arithmetic, Algebra and Geometry Via the Theory of Proportions
- 1. 0488780 - FLU-F 2018 RIV PT eng J - Článek v odborném periodiku
Descartes on the Unification of Arithmetic, Algebra and Geometry Via the Theory of Proportions.
Revista Portuguesa de Filosofia. Roč. 73, č. 3/4 (2017), s. 1239-1258. ISSN 0870-5283
Institucionální podpora: RVO:67985955
Klíčová slova: algebra * Descartes * Euclid * geometry * multiplication * proportion theory * structure
Kód oboru RIV: AA - Filosofie a náboženství
Obor OECD: Philosophy, History and Philosophy of science and technology
In this paper, we explore the role of the theory of proportions in the constitution of Cartesian geometry. Particularly, we intend to show that Descartes used it in an essential way to achieve a unification between geometry and arithmetic. Such a unification occurred mainly by redefining the operation of multiplication in order to include both operations among segments and among numbers. Finally, we question about the significance of Descartes’ algebraic thought. Although the goal of Descartes’ Géométrie is to solve geometric problems, his first readers emphasized the role of algebra as a study of relations.
Trvalý link: http://hdl.handle.net/11104/0283322
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https://roundingcalculator.guru/round-to-the-nearest-singapore-dollar-calculator/
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math
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Make use of our handy and user-friendly Rounding to the Singapore dollar calculator tool to round the given amount to its nearest dollar. Just enter the dollar amount with cents and click on the calculate button to obtain the outcome in Singapore dollars along with steps in less time.
Rounding to the Singapore Dollar Calculator: Here is the ultimate guide that helps to find the rounded value to the nearest Singapore dollar by the best online calculator tool. Also, it makes you learn and understand what does it mean and how to round off to the Singapore dollars by hand. Check all the steps and rules for rounding the currency and practice well with our provided solved examples. Use the Rounding off to the Singapore Dollar Calculator and perform your calculations easier and faster.
The process of removing the cents part in the given Singapore dollar amount using rounding currency rules is called rounding to the Singapore dollar. For example, $4.587 is the given amount where the rounded value to the nearest Singapore dollar is $5.
Here we will be seeing the simple steps to round off the Singapore dollars & cents amount to the Singapore dollar.
Need extra clarity on the process of rounding to the Singapore dollars? Check out the solved examples available and be familiar with manual calculations.
Round $87.234 to the Singapore dollar.
Given dollar amount is S$87.234
Look at the tenth place value and apply the rounding rules to it.
Here, 2 is the digit placed in the tenth position. The digit 2 is less than 5 so round down the amount.
Just keep the ones' digit as it is and remove all digits after the decimal point along with the decimal separator.
Therefore, the rounded amount to the nearest Singapore dollar is $87.
What is S$3.7 rounded to the Singapore dollar?
Given amount is $3.7 SGD
Now, look at the tenth place value in cents.
Here, digit 7 is located in the tenth place.
The value 7 is greater than or equal to 5, so as per the rounding rules we have to round up the amount to the Singapore dollar.
Add 1 to the Singapore dollar and remove the cents part.
Hence, S$4 is the rounded amount to the nearest SGD.
Do visit our website roundingcalculator.guru and refer to the other rounding money calculators for easy calculations & accurate results.
1. What is Singapore Dollar?
The Singapore Dollar is the official currency of Singapore. Basically, it divides into 100 cents. The symbol to represent the Singapore dollar is S$ or $ and the Code is SGD. The subunit of Sing-dollar is Cent (c). Also, it is the thirteen-most traded currency in the world by value from the date of 2019.
2. Where can I find the Rounding to the Singapore Dollar Calculator Online?
You can find the online Rounding to the Singapore Dollar Calculator with steps from roundingcalculator.guru which is a reliable & trusted website.
3. How do you round to SGD?
To round the amount to the nearest SGD, take a look at the first digit after the decimal point in the cents part. If it is >=5 round up to SGD, else if it is <5 round down to SGD.
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https://www.shaalaa.com/question-bank-solutions/a-boy-travels-average-speed-10-m-s-1-20-min-how-much-distance-does-he-travel-types-of-motion-based-on-speed_32872
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math
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A Boy Travels with an Average Speed of 10 M S-1 for 20 Min. How Much Distance Does He Travel ? - Physics
A boy travels with an average speed of 10 m s-1 for 20 min. How much distance does he travel?
Average speed of boy = 10 m s-1
Time taken = 20 min
Distance travelled = Speed × Time taken
Convert minutes into seconds
1 minute = 60 sec.
20 minutes = 20 × 60 = 1200 sec.
Distance travelled = 10 m s-1 × 1200 sec.
= 12000 m Or 12 km
Concept: Types of Motion Based on Speed
Is there an error in this question or solution?
why create a profile on Shaalaa.com?
1. Inform you about time table of exam.
2. Inform you about new question papers.
3. New video tutorials information.
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https://platformdyzt.web.app/livers37530riw/why-interest-rate-represent-the-time-value-of-money-20.html
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math
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Time value of money refers to the fact that a money in pocket today is worth for one year at 100 percent, and we simply mean that $1 today is worth $2 in one In general, if you invest for one period at an interest rate of r, your investment will Time-Value-of-Money (TVM): TI-BA II PLUS Present Value of a single sum. word Enter appears in the display, it means you can enter a different interest rate. In addition, they usually contain a limited number of choices for interest rates we will demonstrate how to find the present value of a single future cash amount, Often, the discount rate is some interest rate that represents the individual's best alternative use for money today. The formula for calculating the present value of 11 Mar 2020 Interest rate used to calculate Net Present Value (NPV) value of cash outflows over a period of time and is represented above by “CF”). Welcome to the lecture series on Time value of money-Concepts and Calculations. Disbursements are represented by arrows directed downward. annual interest rate and cash flow at the end of the year is given and we will call this type.
29 May 2014 Interest rate is the exchange price between the current and future value of the Afghani. 2. Interest rates represent risk and inflation. 4. 4 Time
So at the most basic level, the time value of money demonstrates that all things being equal, it seems better to have money now rather than later. But why is this? A $100 bill has the same value What does the time value of money (TVM) mean? Time value simply means that if an investor is offered the choice between receiving $1 today or receiving $1 in the future, the proper choice will always be to receive the $1 today, because that $1 can be invested in some opportunity that will earn interest. This is the value of the formulas for the present value and the future value of money! Interest Rate Conversions. In investments, pricing and returns are often expressed in interest rates that are compounded in specific time intervals. The actual interest rate or yield will depend on the compounding period. The importance of the Time of Value of Money. Almost everything in life involves the time value of money. If you buy a car on credit, take out a mortgage, or invest in stocks. It all involves the time value of money. If you work for a company, every decision the company makes will involve, in one way or another, the time value of money. Time value of money. Or another way to think about it is, think about what the value of this money is over time. Given some expected interest rate and when you do that you can compare this money to equal amounts of money at some future date. Now, another way of thinking about the time value or, I guess, another related concept to the time value There are technical differences, but both represent a rate of increase in the time value of money. So if the interest rate describes the time value of money, then the higher it is, the more valuable money is in your hands and the less valuable money is down the road. There are multiple reasons that money can be more valuable today than tomorrow. Whenever you are solving any time value of money problem, make sure that the n (number of periods), the i (interest rate), and the PMT (payment) components are all expressed in the same frequency. For example, if you are using an annual interest rate, then the number of periods should also be expressed annually.
Time value of money refers to the fact that a money in pocket today is worth for one year at 100 percent, and we simply mean that $1 today is worth $2 in one In general, if you invest for one period at an interest rate of r, your investment will
Adjusting for "inflation" in the past is not remotely the same as calculating the present or future value of money for a given interest rate. Adjusting for inflation is a Unit 2: Time Value of Money: Future Value, Present Value, and Interest Rates Also, Unit 2 exposes the concept of interest rates and how to apply them This video shows you about what it means to use an annual interest rate continuously.
19 Nov 2014 One, NPV considers the time value of money, translating future cash flows 4% interest on its debt, then it may use that figure as the discount rate. is based on several assumptions and estimates, which means there's lots of
Interest rate (I) - This is the growth rate of your money over the lifetime of the investment. It is stated in a percentage value, such as 8% or .08. Payment amount ( Path to financial security and time value of money. payment, we have the number of periods, and we have the interest rate, which is represented by r here.
The time value of money is a basic financial concept that holds that money in the present is worth more than the same sum of money to be received in the future. This is true because money that you have right now can be invested and earn a return, thus creating a larger amount of money in the future.
There are technical differences, but both represent a rate of increase in the time value of money. So if the interest rate describes the time value of money, then the higher it is, the more valuable money is in your hands and the less valuable money is down the road. There are multiple reasons that money can be more valuable today than tomorrow.
The time periods may represent years, months, days, or any length of time so long as Compounding is the impact of the time value of money (e.g., interest rate)
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https://www.microlinkinc.com/search/gain-deviation
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math
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Keyword Analysis & Research: gain deviation
Keyword Research: People who searched gain deviation also searched
Search Results related to gain deviation on Search Engine
Standard Deviation | A Step by Step Guide with Formulas
DA: 21 PA: 29 MOZ Rank: 50
Deviation of Gain Calculator - agrimetsoft.com
Deviation of Gain. In contrast to R2, there are no significant problems in computing the average DG for periods comprising several years. The coefficient of gain from the daily mean, DG, compares model results with daily mean discharge values, which vary throughout the year. DG can vary between 0 and 1, with 0 being a perfect model (WMO, 1986).
DA: 59 PA: 69 MOZ Rank: 41
Normalized gain: What is it and when and how should I …
Mar 18, 2016 · It normalizes the average raw gain in a population by the standard deviation in individuals’ raw scores. d = ( <post> - <pre> ) / stdev The major mathematical difference between normalized gain and effect size is that normalized gain does not account for the size of the class or the variation in students within the class, but effect size does.
DA: 31 PA: 67 MOZ Rank: 27
INA293: gain deviation - Amplifiers forum - Amplifiers ...
INA293: gain deviation. Alen Barisic. Intellectual 780 points. Part Number: INA293. Other Parts Discussed in Thread: INA190. Hi, we need a programmable current source 1..12mA (2..24V), 50kHz for IEPE sensors. with over voltage protection up to ± 100V. we built 3 prototypes with this circuit.
DA: 27 PA: 15 MOZ Rank: 68
Compute effect size from Mean Gain Scores and Standard ...
The standard deviation of the first group at pre-test. post1mean: The mean of the first group at post-test. post1sd: The standard deviation of the first group at post-test. grp1n: The sample size of the first group. gain1mean: The mean gain between pre and post of the first group. gain1sd: The standard deviation gain between pre and post of the first group. grp1r
DA: 82 PA: 41 MOZ Rank: 23
Downside Deviation Defined - investopedia.com
Nov 14, 2020 · Downside deviation is a measure of downside risk that focuses on returns that fall below a minimum threshold or minimum acceptable return (MAR). It is used in the calculation of the Sortino ratio ...
DA: 61 PA: 55 MOZ Rank: 67
Gain - Teledyne Photometrics
The mean divided by the variance equals the gain: gain = mean /variance. A more rigorous method is that of Mortara and Fowler ( SPIE Vol. 290 Solid State Imagers for Astronomy (1981) pp. 28-33), which essentially involves repeating the above procedure for a series of illumination levels over the full range of the CCD full well.
DA: 3 PA: 46 MOZ Rank: 58
Deviation Handling and Quality Risk Management
Deviation Handling and Quality Risk Management 5 An efficient deviation handling system, should implement a mechanism to discriminate events based on their relevance and to objectively categorize them, concentrating resources and efforts in good quality investigations of the root causes of relevant deviations.
DA: 25 PA: 17 MOZ Rank: 80
What does it mean when an investment has a high downside deviation?
Standard deviation measures volatility on the upside and the downside, which presents a limited picture. Two investments with the same standard deviations are likely to have different downside deviations. Downside deviation can also tell you when a "risky" investment with a high standard deviation is likely safer than it looks.
DA: 88 PA: 26 MOZ Rank: 38
Which is the best way to calculate downside deviation?
The Sortino ratio says that the second one is better, and it quantifies the difference. The first step of calculating the downside deviation is to choose a minimum acceptable return (MAR). Popular choices include zero and the risk-free T-bill rate for the year. We'll just use one here for simplicity.
DA: 69 PA: 100 MOZ Rank: 30
How to calculate the gain of an image?
A simple method to calculate the system gain is shown below: Collect a bias image (zero-integration dark image) and label it “bias”. Collect two even-illumination images and label them “flat1” and “flat2”. Calculate a difference image: diff = flat2 – flat1. Calculate the standard deviation of the central 100 x 100 pixels in the difference image.
DA: 42 PA: 74 MOZ Rank: 89
How to calculate the normalized gain of averages?
Gain of averages: First calculate the average pre-test and average post-test score for your class, then take the normalized gain of these: <g> = (<Post> - <Pre>)/(100 - <Pre>) Average of gains: First calculate the normalized gain for each student, then average these: g ave = <(Post - Pre)/(100 - Pre)>.
DA: 81 PA: 76 MOZ Rank: 45
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http://www.quanty.org/_export/xhtml/documentation/standard_operators/start
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math
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Several standard operators are defined. Once specific spin-orbitals are grouped in shells and we assigned quantum numbers to them operators can be created. The most obvious example is to relate a set of spin-orbitals to an atomic like shell with a radial wave-function times an angular dependent part that is given by the spherical Harmonics. In this case we can talk about the angular momentum and Coulomb interaction in terms of Slater integrals. Although for real molecules and solids the important Wannier orbitals are not given as spherical functions, one very often can take spherical functions as a basis set. (The Gaussian basis set for example works with atom centered spherical harmonic times a radial wave-function).
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http://www.oceansonline.com/simplemath.html
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Why are we afraid of math? It is one of the most useful tools we could ever learn. It's like being afraid of your car. Imagine where you would be without that and you have some idea of what it's like to go through life being afraid of simple math.
Here are some good reasons to learn math:
to figure out how much you need to earn to 1) move out of your parent's house; 2) move closer to the beach; 3) move in with your boyfriend or girlfriend; 4) buy your own island in the South Pacific
to figure out how many months it will take you to save up enough money to 1) buy the new Blink 182 CD; 2) buy the Pink Floyd collection; 3) buy every Frank Sinatra record ever made; 4) start your own record company
to figure out how long it will take you to 1) drive to Vegas in your Dad's Dodge Dart; 2) drive to Reno in your Mom's new BMW; 3) drive to Nashville for the Country Music Awards in your rented Chevy Tracker; 4) drive across the ocean in a stolen Humvee
to figure out the percentage of your time that you spend 1) thinking about moving out; 2) trying to sing like Frank Sinatra; 3) begging your mom to let you drive her new BMW; 4) surfing the web instead of doing your oceanography homework.
Math surrounds us. It involves nearly everything we do on a daily basis. Don't believe me? Take this questionnaire.
The Do You Need to Know Math Questionnaire?
If you answer yes to any one of these questions, then you need to know math.
Do you ever shop (for anything)?
Have you ever dreamed of being rich and famous?
Have you ever had or ever want to have sex?
Do you want to pass this oceanography course?
I bet you answered yes to one of those questions. If not then I'm wrong. But regardless, the only really important question to your life right now should be the last one (okay, yes, I'm joking, shopping is important, too). And while I will tell you right here and now that you could still make a decent grade and not know any math, imagine how fine your life will be by knowing a little math!
These math questions are designed to prepare you a little for some of the kinds of math that we will encounter in this course. Rather than wait until we get to those parts of the semester and let you freak out, I'm trying to get the freak going right now so that by the time we get to those important math-oriented sections of the course, you will have calmed down a bit and sharpened your skills enough so that those sections are a piece of cake.
Now, the kind of math you need to know is really quite simple and fairly limited. This isn't a math class. But I hate that deer-in-the-headlights look when I teach tides or waves (one of my favorites and yours) and ask students to 1) add; 2) subtract; 3) multiply; 4) divide; 5) change units; 6) manipulate simple equations. For some reason, many students are simply stunned by these simple math problems.
I'm not going to teach you basic math here. Rather, this section is designed to let you determine whether you need help with math. If you don't understand these simple problems, then seek help. Come talk to me or enroll in a math class. Find a tutor. Buy a basic math book. Please. Don't rob yourself of one of the most powerful tools known to man. You can bet that banks and credit card companies would love it if no one knew math. Don't let them get the best of you.
You will see versions of these math puzzles on virtually every exam. Make sure you work through them and understand them.
1. You are an ordinary seaman on a ship located at the intersection of the equator and the international date line. You desperately want to move up in ranks because you are tired of cleaning toilets. Your chance comes when the navigator falls overboard while looking at jellyfish. His last words are "One degree of latitude equals 60 nautical miles." A day goes by. The Captain tells you that the ship has sailed sixty (60) nautical miles due east since the tragic accident. If you can tell him the ship's new position, you get the job. What is the ship's new longitude and latitude? (Hint: think about what you need to know to answer this question. Look back through your notes to find the key information.)
2. The Captain, a demanding sort, now wants to know the depth of the water. He gives you a Toys-R-Us Sonar Unit, good enough to report the time it takes a sound pulse to travel from the ship to the bottom and back, but not good enough to calculate the distance. You remember from your oceanography class at Fullerton College that sound travels at approximately 1500 meters per second. You set up the Sonar unit, hit the go button, it pings and 12 seconds later the ping returns. How deep is the bottom in meters?
3. The Captain has an old chart with soundings in miles. Now he wants to know how deep is the bottom in miles. The ship hasn't moved since your first sounding and the ping returns after 12 seconds. How deep is the bottom in miles?
4. The Captain gets a weather report over the weather fax. A storm north of you covers a rectangular area 1000 miles long and 200 miles wide. To learn something about the kinds of waves generated by the storm, the Captain wants to estimate the area over which the storm blows, something known as the fetch. He asks you to calculate the area of the storm given the information in the weather fax. What is the fetch of the storm in square miles?
5. The storm front is approximately 3409 miles due north of the ship. It generates waves traveling due south at 50 feet per second. How many days will it take the waves to reach the ship?
6. The Captain hands you an obscure equation and gives you no clue as to what it means. S=L/T or S equals L divided by T. He asks you to give him a new equation that expresses T in terms of S and L, or T=? What does T equal? (In other words, solve this equation for T.)
7. Woops. He made a mistake. He wants you to solve it for L, or L=? What does L equal, in terms of S and T?
8. The Captain finally reveals to you that this is a speed equation for waves, where S, the speed of the wave is equal to L/T (he won't tell you what they mean!). He reminds you that the waves from the storm are traveling at 50 feet per second and he tells you that T=10 seconds. What does L equal? (Don't forget the units.)
9. The ship finally makes it near shore. The Captain wants to know whether the tides will affect the ship's entry through the harbor. He asks you to compute the difference between the high tide and the low tide. He tells you that the high tide is 6 feet above sea level and that the low tide is 1 foot below sea level (or -1 foot). Compute the difference: 6 - (-1) = ?
10. You finally get off the ship and are dying to go to Vegas but you only have $50 bucks. You can drive your Dodge Dart, which gets 20 miles to the gallon and maxes out at 50 miles per hour; or you can drive your mom's new BMW, which only gets 10 miles to the gallon but goes 150 miles per hour. Gas will cost you a buck a gallon but food will cost you $10 every three hours. Vegas is 400 miles from your port. Which car do you take? Remember, you want the most money possible to gamble in Vegas.
The answers to the Oceanography Math Puzzles will be discussed in the Forums.
These web sites have some great and simple math problems that will really help sharpen your math skills. I suggest giving them a try if you felt a little rusty with the above problems. Don't feel bad if you have to venture into lower K-12 to find problems that you can solve. That's what these math lessons are all about. Please feel free to e-mail me if you have any questions.
Girls to the Fourth Power
University of Hawaii Quiz Center
Marmalade_Man's Fantastic Math Tricks
Dave's Math Tables
The Math Forum
Frequently Asked Questions about Blackjack
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https://www.gc.cuny.edu/Page-Elements/Academics-Research-Centers-Initiatives/Doctoral-Programs/Mathematics
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The staff of the Math Program Office are working remotely and fully operational while the office is physically closed until further notice. Use e-mail to contact any of us.
The Graduate Center's Ph.D. Program in Mathematics is a crossroads for the many research mathematicians working in the City University of New York, as well as a place for doctoral students to gain the background they will need to pursue careers as pure or applied mathematicians. The Graduate Center is the only campus offering a doctoral degree in mathematics and the majority of our faculty have dual appointments at the Graduate Center and at one of four year colleges within the CUNY system.
Research areas include algebraic geometry, algorithms, combinatorics, complex analysis and Teichmuller theory, dynamics, group theory, Lie theory, logic, number theory, probability, Riemannian geometry and analysis, and topology.
Executive Officer, Professor
Deputy Executive Officer
Assistant Program Officer
Einstein Chair Secretary
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https://settheory.mathtalks.org/seminar-in-logic-set-theory-and-topology-november-6/
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math
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The next meeting of the seminar in Logic, Set Theory and Topology will be held on Tuesday, November 6.
Time is 16:00 – 17:30.
Place: seminar room 201 which is located in the building of Computer Science Department (not Math Dept)
Speaker :Asaf Karagila (BGU)
Title: On the ordering of cardinals without choice.
Abstract: We will discuss the definitions of cardinals without the axiom of choice, and we shall see two naturally occurring orders on cardinals.
We shall see examples as for why these orderings need not be the same without the axiom of choice.
The material also appears on the following page.
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https://plainmath.net/90062/you-wish-to-estimate-with-99-confidence
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math
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Given a vector x in the n=6-dimensional Euclidian space , do there exist n−1 continuous functions to such that the matrix
is invertible for all x in .
I am aware of the results of
T. Wazewski, Sur les matrices dont les elements sont des fonctions continues. Composito Mathematica, tome 2 (1935), p. 63-68
B Eckmann, Mathematical survey lectures 1943-2004. Springer 2006.
There may be no topological obstruction for n=6 while there may be for n unusual. I know the answer for n=2 and four. it is based totally on diversifications with appropriate signs and symptoms in an effort to make orthogonal to x. this doesn't paintings for n=6. as a result the question for n=6 or even large n=8, …
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https://www.semanticscholar.org/paper/Commuting-holonomies-and-rigidity-of-holomorphic-f-Movasati-Nakai/c84453fa647daccebfef9e4546e314dea6e32b64
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math
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In this article we study deformations of a holomorphic foliation with a generic non-rational first integral in the complex plane. We consider two vanishing cycles in a regular fiber of the first integral with a non-zero self intersection and with vanishing paths which intersect each other only at their start points. It is proved that if the deformed holonomies of such vanishing cycles commute then the deformed foliation has also a first integral. Our result generalizes a similar result of Ilyashenko on the rigidity of holomorphic foliations with a persistent center singularity. The main tools of the proof are Picard-Lefschetz theory and the theory of iterated integrals for such deformations.
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https://www.physicsforums.com/threads/find-the-change-of-internal-energy-of-the-air.815400/
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math
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1. The problem statement, all variables and given/known data A car rubber has the volume 50 liters when it is bloated in a pressur 1.8 atm and in a temperature 293 K. After some hours of journey as an effect of friction the pressure will become 2atm. Find the change of internal energy of the air inside the rubber (U) 2. Relevant equations U=3/2nRT 3. The attempt at a solution I thought to sue the formula U=3/2nRT, but I don't know the n.
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https://www.proprofs.com/quiz-school/story.php?title=shot-list-short-cuts
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math
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In mathematics, an ____________ is a segment of the circumference of a circle. A camera arc is similar — the camera moves in a rough semi-circle around the subject.
In many circles, a ____________ shot is also known as a tracking shot or trucking shot. However, some professionals prefer the more rigid terminology which defines dolly as ____ and-_______ movement (i.e. closer/further away from the subject), while tracking means _____ to ______ movement.
Most dollies have a lever to allow for vertical movement as well (known as a _______ move).
The rule states that an image should be imagined as divided into nine equal parts by two equally-spaced horizontal lines and two equally-spaced vertical lines, and that important compositional elements should be placed along these lines or their intersections. What rule is this?
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http://www.solutioninn.com/structural-formulas-for-all-the-constitutionally-isomeric
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math
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Question: Structural formulas for all the constitutionally isomeric
Write structural formulas for all the constitutionally isomeric compounds having the given molecular formula.
Answer to relevant QuestionsElectron delocalization can be important in ions as well as in neutral molecules. Using curved arrows, show how an equally stable resonance structure can be generated for each of the following anions: 4 figures of part a-d ...Describe the bonding in methylsilane (H3CSiH3), assuming that it is analogous to that of ethane. What is the principal quantum number of the orbitals of silicon that are hybridized?Write a Lewis structure for each of the following organic molecules All the Diagrams are included in the SolutionWrite structural formulas for all the constitutionally isomeric compounds having the given molecular formula. (a) C4H10 (d) C4H9Br (b) C5H12 (e) C3H9N (c) C2H4Cl2Select the compounds in Problem 1.43 in which all the carbons are (a) sp3-hybridized (b) sp2-hybridized do any of the compounds in Problem 1.43 contain an sp-hybridized carbon?
Post your question
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http://www2.cs.uh.edu/~jhuang/JCH/LD/chap07.html
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math
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(See Chapter 7 of Mano's Digital Design (2nd ed.))
7-1 Include a 2-input NAND gate with the register of Fig. 7-1 and connect the gate output to the CP inputs of all the flip-flops. One input of the NAND gate receives the clock pulses from the clock-pulse generator. The other input of the NAND gate provides a parallel-load control. Explain the operation of the modified register.
Some assumption about the behavior of the flip-flops must be made before we can determine the function of this register.
In accordance with the discussion given in the second paragraph on page 259, it is assumed that the flip-flop changes its state on the positive edge of a clock pulse. That means each flip-flop will respond to its input when a clock pulse is ended. That implies that the new content will not be available until the arrival of the next clock pulse.
Therefore, we may say that this register allows parallel input, and provides one unit of time delay.
7-2 Change the synchronous-clear circuit in the register of Fig. 7-2. The modified register will have a parallel-load capability and a synchronous-clear capability, but no asynchronous-clear circuit. The retister is cleared synchronously when the clock pulse in the CP input goes through a negative transition provided R = 1 and S = 0 in all the flip-flops.
It can be done in many ways. One possibility is to modify each flip-flop control circuit as indicated below:
7-4 Design a sequential circuit whose state diagram is given in Fig. 6-31 using a 3-bit register and a 16 x 4 ROM.
Connect a 3-bit register and a 16x4 ROM as depicted below. Treat each bit of the register as a D flip-flop and design the circuit as usual.
7-6 What is the difference between a serial and parallel transfer? Explain how to convert serial data to parallel and parallel data to serial. What type of register is needed?.
In a serial transfer, the data is transferred in sequence one bit at a time (per clock period, if it is synchronous), whereas in a parallel transfer, all bits are transferred at the same time. A shift register can be used to do serial to parallel or parallel to serial transfer as depicted below.
7-12 The 2's complement of a binary number can be formed by leaving all least significant 0's and the first 1 unchanged and complementing all other higher significant bits. Design a serial 2's complementer using this procedure. The circuit needs a shift register to store the binary number and an RS flip-flop to be set when the first least significant 1 occurs. An exclusive-OR gate can be used to transfer the unchanged bits or complement the bits.
7-13 Draw the logic diagram of a 4-bit binary ripple counter using flip-flops that triggle on the positive-edge transition.
It should be drawn as in Fig. 7-12, except that Q' output (instead of Q output) should be used to drive the next flip-flop.
7-14 Draw the loogic diagram of a 4-bit binary ripple down-counter
using the following:
(a) Flip-flops that trigger on the positive-edge transition of the clock.
(b) Flip-flops that trigger on the negative-edge transition.
(a) Same as Fig. 7-12. (b) Same as Fig. 7-12 except Q' instead of Q is used to drive the next flip-flop.
7-15 Construct a BCD ripple counter using a 4-bit binary ripple counter that cann be cleared asynchronously and an external NAND gate. .
Connect the output of the following NAND gate to the CLEAR input of every flip-flop.
7-19 Design a 4--bit binary ripple counter with D flip-flops.
Use D flip-flops to construct T flip-flops as discussed elsewhere. Then interconnect the T flip-flops so obtained as depicted in Fig. 7-12.
7-21 Modify the counter of Fig. 7-18 so that when both the up and down control inputs are equal to 1, the counter does not change state, but remains in the same count.
7-22 Verify thhe flip-flop input functions of the synchronous BCD counter specified in Table 7-5. Draw the logic diagram of the BCD counter and include a count-enable control input.
(1) Construct the Karnaugh map of each input function and simplify it. (2) Provide the count-enable input by using the following circuit.
7-25 Construct a BCD counter using the circuit specified in Fig. 7-19 and an AND gate.
7-26 Construct a mod-12 counter using the circuit of Fig. 7-19. Give two alternatives.
7-27 Using two circuits of the type shown in Fig. 7-19, construct a binary counter that counts from 0 throught binary 64.
7-28 Using a start signal as in Fig 7-21, construct a word-time control that stays on for a period of 16 clock pulses.
7-29 Add four two-input AND gates to the circuit of Fig. 7-22(b). One input in each gate is connected to one output of the decoder. The other input in each gate is connected to the clock. Label the outputs of the AND gate as P0, P1, P2, P3. Show the timing diagrm of the four P outputs.
7-30 Show the circuit and the timing diagram for generating six repeated timing signals, T0 through T5.
7-31 Complete the design of a Johnson counter showing the outputs of the eight timing signals using eight AND gates.
7-32 Construct a Johnson counter for ten timing signals.
COSC 3410 Answers to Selected Problems, Chapter | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
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http://www.blackberryforums.com/27169-post6.html
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math
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Originally Posted by bfrye
That would be part of your data plan (web portion)
Do all the IM clients ( WeMessenger, Verichat, BerryVine Messenger etc.) use the same amount of data when conducting a conversation? Since these programs have different fee structures, are some better value than others, strictly on an "data efficiency" standpoint?
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https://rockasaurus.club/what-do-the-3-4-and-4-4-numbers-mean/
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math
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Asked by: Walter Wellman
The bottom number of a time signature tells you how many beats are in a measure. So, 3/4 means there are three beats per measure, and 4/4 means there are four beats per measure. The top number in a time signature tells you which type of note gets one beat.
What does the 4 in 3/4 mean in music?
Though there are many time signatures that composers can use, below are the most common ones you’ll see in Western music. 2/4: Two quarter-note beats per measure. 3/4: Three quarter-note beats per measure. 4/4: Four quarter-note beats per measure. Also known as common time and notated with a “C.”
What does the 3 over 4 mean?
4. or in a line of text as one number with a slash or solidus then the other number, like this: 3/4. The fraction 3/4 or three quarters means 3 parts out of 4. The upper number, 3, is called the numerator and the lower number, 4, is the denominator.
What does the 4 4 mean?
November 30, 2019. The term 4×4 means a four-wheel-drive vehicle. Technically, the first digit is the number of wheels and the second is the number that are driven, so a four-wheel-drive pickup truck is a 4×4; a rear-wheel-drive one is a 4×2. Related: AWD Vs.
What does a 3/4 time signature mean?
The 3/4 time signature means there are three quarter notes (or any combination of notes that equals three quarter notes) in every measure. As we learned in the prior lesson, because there is a 4 on the bottom, the quarter note gets the beat (or pusle). The 3/4 time signature is sometimes called waltz time.
What is the difference between 4 4 time and 3/4 time?
A 4/4 time signature has four quarter-note beats per measure, whereas a 3/4 time signature has three quarter-note beats per measure.
What do the numbers on a music staff mean?
The top number of the time signature tells you how many beats to count. This could be any number. Most often the number of beats will fall between 2 and 12. The bottom number tells you what kind of note to count. That is, whether to count the beats as quarter notes, eighth notes, or sixteenth notes.
What’s the meaning of 1 2?
One half is the irreducible fraction resulting from dividing one by two (2) or the fraction resulting from dividing any number by its double. Multiplication by one half is equivalent to division by two, or “halving”; conversely, division by one half is equivalent to multiplication by two, or “doubling”.
What does 4 mean?
“More than Love (see <3)" is the most common definition for <4 on Snapchat, WhatsApp, Facebook, Twitter, Instagram, and TikTok.
What is 3/4th called?
3/4 or ¾ may refer to: The fraction (mathematics) three quarters (3⁄4) equal to 0.75.
What does the lower number 4 mean in 3/4 time signature?
The time signature 3/4 tells a musician that a quarter note represents one beat in a measure (the lower number) and that there will be three beats in each measure (the top number).
How do you read a time signature?
And music time signatures are made up of two numbers a top number and a bottom number the number on the bottom tells us the type of note the time signature is referring to a.
How many beats is a 3/4 bar?
We already know how many beats in a bar the 3 quarter time signature has: that’s 3 beats, or 3 quarter notes. But any other combination of note lengths can be made that add up to 3 quarter notes, of course. So, 1 quarter note plus 4 eighth notes, or 2 quarter notes and 2 eighth notes, etcetera.
How do I count bars in a song?
Basically what you're doing is just switching the first number in that count. And basically every time that you switch that number you're switching the bars.
How do you read music bars?
Each bar is divided by a bar line bar lines are the lines that separate each bar. In this example there are three regular bar lines.
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https://www.hindawi.com/journals/amp/2018/4523512/
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math
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Research Article | Open Access
Ximin Liu, Ning Zhang, "Spacelike Hypersurfaces in Weighted Generalized Robertson-Walker Space-Times", Advances in Mathematical Physics, vol. 2018, Article ID 4523512, 6 pages, 2018. https://doi.org/10.1155/2018/4523512
Spacelike Hypersurfaces in Weighted Generalized Robertson-Walker Space-Times
Applying generalized maximum principle and weak maximum principle, we obtain several uniqueness results for spacelike hypersurfaces immersed in a weighted generalized Robertson-Walker (GRW) space-time under suitable geometric assumptions. Furthermore, we also study the special case when the ambient space is static and provide some results by using Bochner’s formula.
In recent years, spacelike hypersurfaces in Lorentzian manifolds have been deeply studied not only from their mathematical interest, but also from their importance in general relativity.
Particularly, there are many articles that study spacelike hypersurfaces in weighted warped product space-times. A weighted manifold is a Riemannian manifold with a measure that has a smooth positive density with respect to the Riemannian one. More precisely, the weighted manifold associated with a complete -dimensional Riemannian manifold and a smooth function on is the triple , where stands for the volume element of . In this setting, we will take into account the so-called Bakry-Émery Ricci tensor (see ) which as an extension of the standard Ricci tensor , which is defined by Therefore, it is natural to extend some results of the Ricci curvature to analogous results for the Bakry-Émery Ricci tensor. Before giving more details on our work we present a brief outline of some recent results related to our one.
In , Wei and Wylie considered the complete -dimensional weighted Riemannian manifold and proved mean curvature and volume comparison results on the assumption that the -Bakry-Émery Ricci tensor is bounded from below and or is bounded. Later, Cavalcante et al. researched the Bernstein-type properties concerning complete two-sided hypersurfaces immersed in a weighted warped product space using the appropriated generalized maximum principles. Moreover, obtained new Calabi-Bernstein’s type results related to complete spacelike hypersurfaces in a weighted GRW space-time. More recently, some rigidity results of complete spacelike hypersurfaces immersed into a weighted static GRW space-time are given in .
In this paper we study spacelike hypersurfaces in a weighted generalized Robertson-Walker (GRW) space-times. Moreover, a GRW space-time is a space-time regarding a warped product of a negative definite interval as a base, a Riemannian manifold as a fiber, and a positive smooth function as a warped function. Furthermore, there exists a distinguished family of spacelike hypersurfaces in a GRW space-time, that is, the so-called slices, which are defined as level hypersurfaces of the time coordinate of the space-time. Notice that any slice is totally umbilical and has constant mean curvature.
We have organized this paper as follows. In Section 2, we introduce some basic notions to be used for spacelike hypersurfaces immersed in weighted GRW space-times. In Section 3, we prove some uniqueness results of spacelike hypersurface in a weighted GRW space-time under appropriate conditions on the weighted mean curvature and the weighted function by using the generalized Omori-Yau maximum principle or the weak maximum principle. Finally, in Section 4, applying the weak maximum principle, we obtain some rigidity results for the special case when the ambient space is static.
Let be a connected -dimensional oriented Riemannian manifold and be an open interval in endowed with the metric . We let be a positive smooth function. Denote to be the warped product endowed with the Lorentzian metric where and are the projections onto and , respectively. This space-time is a warped product in the sense of , with fiber , base , and warping function . Furthermore, for a fixed point , we say that is a slice of . Following the terminology used in , we will refer to as a generalized Robertson-Walker (GRW) space-time. Particularly, if the fiber has constant section curvature, it is called a Robertson-Walker (RW) space-time.
Recall that a smooth immersion of an -dimensional connected manifold is called a spacelike hypersurface if the induced metric via is a Riemannian metric on , which will be also denoted for .
In the following, we will deal with two particular functions naturally attached to spacelike hypersurface , namely, the angle (or support) function and the height function , where is a (unitary) timelike vector field globally defined on and is a unitary timelike normal vector field globally defined on .
Let and stand for gradients with respect to the metrics of and , respectively. By a simple computation, we have Therefore, the gradient of on is Particularly, we have where denotes the norm of a vector field on .
Now, we consider that a GRW space-time is endowed with a weighted function , which will be called a weighted GRW space-time . In this setting, for a spacelike hypersurface immersed into , the -divergence operator on is defined by where is a tangent vector field on .
For a smooth function , we define its drifting Laplacian by and we will also denote such an operator as the -Laplacian of .
According to Gromov , the weighted mean curvature or -mean curvature of is given by where is the standard mean curvature of hypersurface with respect to the Gauss map .
It follows from a splitting theorem due to Case (see Theorem ) that if a weighted GRW space-time is endowed with a bounded weighted function such that for all timelike vector fields on , then must be constant along . In the same spirit of this result, in the following we will consider weighted GRW space-times whose weighted function does not depend on the parameter ; that is, . Moreover, for simplicity, we will refer to them as .
In the following, we give some technical lemmas that will be essential for the proofs of our main results in weighted GRW space-times (for further details on the proof, see Lemma in ).
Lemma 1. Let be a spacelike hypersurface immersed in a weighted GRW spacetime , with height function . Then,
If we denote as the space of the integrable functions on with respect to the weighted volume element , using the relation of and Proposition in , we can obtain the following extension of a result in .
Lemma 2. Let be a smooth function on a complete weighted Riemannian manifold with weighted function such that does not change sign on . If , then vanishes identically on .
In the following, we will introduce the weak maximum principle for the drifted Laplacian. By the fact in , that is, the Riemannian manifold satisfies the weak maximum principle if and only if is stochastically complete, we can have the next lemma which extended a result of .
Lemma 3. Let be an -dimensional stochastically complete weighted Riemannian manifold and be a smooth function which is bounded from below on . Then there is a sequence of points such that Equivalently, for any smooth function which is bounded from above on , there is a sequence of points such that
3. Uniqueness Results in Weighted GRW Space-Times
In this section, we will state and prove our main results in weighted GRW space-times . We point out that, to prove the following results, we do not require that the -mean curvature of the spacelike hypersurface is constant.
Recall that a slab of a weighted GRW spacetime is a region of the type
Theorem 4. Let be a weighted GRW spacetime which obeys . Let be a complete spacelike hypersurface that lies in a slab of . If the -mean curvature satisfies and , then is a slice of .
Proof. From (10), we have By the hypotheses, we have . Moreover, since lies in a slab, there is a positive constant such that Therefore, we can apply Lemma 2 to get ; that is, is constant. Therefore is a slice.
Theorem 5. Let be a weighted GRW spacetime which obeys . Let be a complete spacelike hypersurface that lies in a slab of . If the -mean curvature satisfies and , then is a slice of .
Proof. By a similar reasoning as in the proof of Theorem 4, we have where the last inequality is due to .
Taking into account the assumptions, we have . Now in the same argument as in Theorem 4, we have that is a slice.
Next, we will use the weak maximum principle to study the rigidity of the spacelike hypersurfaces in weighted GRW space-times.
Theorem 6. Let be a weighted GRW spacetime which satisfies and there is a point such that . Let be a stochastically complete constant -mean curvature spacelike hypersurface such that , which is contained in a slab; then is -maximal. In addition, if is complete and , then is a slice.
Proof. We take the Gauss map of the hypersurface such that ; from (7) we have .
By Lemma 3, the weak maximum principle for the drifted Laplacian holds on ; then there exist two sequences such that On the other hand, from (9), we have Since lies in a slab, if is bounded from below, then Moreover, if is bounded from above, we get Considering that the function is increasing, then Hence, ; that is, is a -maximal spacelike hypersurface. Using (10), we have In the following, by the same argument as in Theorem 4, we have that is a slice.
4. Weighted Static GRW Space-Times
In this section, we obtain some rigidity results of stochastically complete hypersurfaces in weighted static GRW space-times by the weak maximal principle. Firstly, we give the following technical result which extended the corresponding conclusion in .
Lemma 7. Let be a stochastically complete Riemannian manifold and be a nonnegative smooth function on . If there exists a positive constant such that , then .
Theorem 8. Let be a stochastically complete hypersurface with constant -mean curvature in a weighted static GRW spacetime . Assume that for some positive constant and the weighted function is convex. If for some constant , then is a slice.
Proof. Let be a (local) orthonormal frame in ; using the Gauss equation, we have that for . Moreover, we also have where is the sectional curvature of the fiber and and are the projections of the tangent vector fields and onto .
By a direct computation and considering the hypothesis , we get Substituting (25) into (23), Furthermore, taking into account that the weighted function is convex, we have Therefore, In particular, we have Now we recall the Bochner-Lichnerowicz formula (see ): From the fact that is a constant, we have By , we get Using (29), (31), and (32) in (30), we have Finally, considering the hypothesis , we obtain Thus, there is a positive constant such that Therefore, is constant by Lemma 7.
Theorem 9. Let be a stochastically complete hypersurface with constant -mean curvature in a weighted static GRW space-time . Assume that the sectional curvature is nonnegative and the weighted function is convex. If is bounded from above, then is -maximal.
Proof. As in the proof of Theorem 8, taking into account that the hypothesis is nonnegative, there is a constant such that Moreover, considering the relation , we have Using (9) and (37), we obtain By the hypothesis that is bounded from above, applying Lemma 3, the weak maximum principle, we get Therefore is -maximal.
As a consequence of the proof of Theorem 8, we can get the following corollary.
Corollary 10. Let be a stochastically complete hypersurface with constant -mean curvature in a weighted static GRW space-time . Assume that and for some positive constants and . If for some constant , then is a slice.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
This work is supported by National Natural Science Foundation of China (no. 11371076).
- D. Bakry and M. Mery, “Diffusions hypercontractives,” in Sminaire de probabilits, XIX, vol. 1123 of Lecture Notes in Math., pp. 177–206, Springer, Berlin, Germany, 1983.
- G. Wei and W. Wylie, “Comparison geometry for the Bakry-Emery Ricci tensor,” Journal of Differential Geometry, vol. 83, no. 2, pp. 377–405, 2009.
- M. P. Cavalcante, H. F. de Lima, and M. S. Santos, “On Bernstein-type properties of complete hypersurfaces in weighted warped products,” Annali di Matematica Pura ed Applicata. Series IV, vol. 195, no. 2, pp. 309–322, 2016.
- M. P. Cavalcante, H. F. de Lima, and M. S. Santos, “New Calabi-Bernstein type results in weighted generalized Robertson-Walker spacetimes,” Acta Mathematica Hungarica, vol. 145, no. 2, pp. 440–454, 2015.
- H. F. de Lima, A. M. Oliveira, and M. S. Santos, “Rigidity of complete spacelike hypersurfaces with constant weighted mean curvature,” Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry, vol. 57, no. 3, pp. 623–635, 2016.
- B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, San Diego, Calif, USA, 1983.
- L. J. Alas, A. Romero, and M. Sánchez, “Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes,” General Relativity and Gravitation, vol. 27, no. 1, pp. 71–84, 1995.
- M. Gromov, “Isoperimetry of waists and concentration of maps,” Geometric and Functional Analysis, vol. 13, no. 1, pp. 178–215, 2003.
- J. S. Case, “Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor,” Journal of Geometry and Physics, vol. 60, no. 3, pp. 477–490, 2010.
- A. Caminha, “The geometry of closed conformal vector fields on Riemannian spaces,” Bulletin of the Brazilian Mathematical Society. New Series. Boletim da Sociedade Brasileira de Matem\'atica, vol. 42, no. 2, pp. 277–300, 2011.
- S. T. Yau, “Some function-theoretic properties of complete Riemannian manifold and their applications to geometry,” Indiana University Mathematics Journal, vol. 25, no. 7, pp. 659–670, 1976.
- S. Pigola, M. Rigoli, and A. G. Setti, “A remark on the maximum principle and stochastic completeness,” Proceedings of the American Mathematical Society, vol. 131, no. 4, pp. 1283–1288, 2003.
- M. Rimoldi, Rigidity Results for Lichnerowicz Bakry-Émery Ricci Tensors [Ph.D. thesis], Università degli Studi di Milano, Milano, Italy, 2011.
- J. M. Latorre and A. Romero, “Uniqueness of noncompact spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes,” Geometriae Dedicata, vol. 93, pp. 1–10, 2002.
Copyright © 2018 Ximin Liu and Ning Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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https://math.answers.com/Q/What_is_the_Second_derivative_of_natural_logarithm_of_square_root_of_X
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math
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3/(4*square root(x)) ....Mukesh
the derivative is 0. the derivative of a constant is always 0.
The derivative of sqrt(2) is zero.
The square root of any number which is not a perfect square;The cube root of any number which is not a perfect cube;Pi, the circular constant.e, the natural logarithm base number.
The square root of x = x to the power of a half
Take the logarithm of 500, half it, then take the antilog.
Take its logarithm, divide that by 2 and take the antilog of your answer....
Use the formula for the derivative of a power. The square root of (x-5) is the same as (x-5)1/2.
It is negative one divided by 4 multiplied by x to the power of 1.5 -1/(4(x^1.5))
The derivative of ANY constant expression - one that doesn't depend on variables - is zero.
There are an infinite number of irrational numbers. Here are some: e (the base for natural logarithms), pi, sqrt(2), sqrt(3), sqrt(5), square root of any number that is not a perfect square: perfect squares are 12 22 32 42 52 etc. which equals 1 4 9 16 25 ..... natural logarithm of any rational number (greater than zero) will be irrational. but not 1, since ln(1) = 0, which is not irrational. Note the logarithm of a negative number is a complex number, and the logarithm of zero is negative infinity.
the product rule is included in calculus part.Product Rule : Use the product rule to find the derivative of the product of two functions--the first function times the derivative of the second, plus the second function times the derivative of the first. The product rule is related to the quotient rule, which gives the derivative of the quotient of two functions, and the chain rule, which gives the derivative of the composite of two functionsif you need more explanation, i want you to follow the related link that explains the concept clearly.
The derivative, with respect to x, is -x/sqrt(1-x2)
The derivative of any constant - any expression that does not involve the independent variable - is zero.
The simplest way to do it is to use Logarithms, from a book of Logarithmic Tables and Anti-logarithms. You simply look up the Logarithm of your quantity, then divide that quantity by 2 , and then look up its Anti-logarithm. that will give you the answer.
There is nothing to solve because there is no = sign.
sqrt(X) is also X^1/2 use power rule 1/2X^-1/2 ( first derivative ) -1/4X^-3/2 ( second derivative ) and so on
You should take the DERIVATIVE of the number or equation
Usually at the minimum or maximum of a function, one of the following conditions arises:The derivative is zero.The derivative is undefined.The point is at the end-points of the domain that is being considered (or of the naturally-defined domain, for example, zero for the square root).This will give you "candidate points"; to find out whether each of these candidate points actually is a maximum or a minimum, additional analysis is required. For example, if the second derivative is positive, you have a minimum, if the second derivative is negative, you have a maximum - but if it is zero, it may be a maximum, a minimum, or neither.
to get the logarythm of a number you must first find the square root of the number and then times it by the original number
Derivative with respect to 'x' of (5x)1/2 = (1/2) (5x)-1/2 (5) = 2.5/sqrt(5x)
1: Calculate the square root, then calculate its square root; OR 2: Take the logarithm of the number, divide it by 4 then take the antilog.
No - a natural number is a whole number. Therefore, the square root of 49 is a natural number, but the square root of 50 is not.
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https://forums.examsbook.com/topic/3226/is-a-square-a-rhombus
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math
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Answer : 1 TRUE Explanation : Answer: A) TRUE Explanation: Yes, a square is a rhombus. But a rhombus is not a square unless the interior angles are at right angles. We know that, a square is a quadrilateral with all sides equal and all the interior angles are 90 deg i.e, at right angles. Whereasa rhombus is also a quadrilateral with all sides equal but the interior angles are not at right angles. Hence, if the interior angles of a rhombus are all at right angles (90 deg), then it is square.
Click here to see the full blog post
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https://www.physicsforums.com/threads/answer-to-2-x-2-3-dx.151377/
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math
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\ 2/(x-2)^3 dx
Basically integrating a perfect cube in the denominator with a constant in the numerator
The Attempt at a Solution
i thought it would be a form of ln(x), but then, that would mean having atleast some x terms in the numerator which are not there, so, how do i do this? Is there a known pre-fixed solution for these things? Like exp(something)?
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https://quizlet.com/130317812/calculus-unit-2-derivatives-overview-flash-cards/
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math
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Calculus Unit 2 Derivatives Overview
Terms in this set (46)
Formula for the Derivative by the Limit Process
The formula for the deriative by the limit process comes from...
The tangent line problem
y - y₁=m(x - x₁)
If an equation is NOT continuous, then it is ____ _________.
If an equation has a sharp turn, then it is _____ ____________.
If an equation has a vertical tangent line, then it is ______ ______________
An equation must be ______________ to be differentiable, but being _____________ does not guarantee differentiablility.
A derivative is a graph of the ___________ of the _________ line at each point.
d/dx means taking the derivative with _________ to ____.
The derivative of a constant is always = _____
Sum Rule: d/dx[f(x) + g(x)]=
f'(x) + g'(x)
Difference Rule: d/dx[f(x) - g(x)]=
f'(x) - g'(x)
Power Rule: d/dx[ xⁿ]=
You can only use the power rule when the variable is in the _____________
You can only use the power rule when there are NOT ________ NOR _________ of variables
You can only use the power rule when there are NOT _________ outside a parenthesis that would cause a variable to have a higher degree
The derivative of position is
The derivative of velocity is
s(t) usually represents
s'(t) usually represents
s''(t) usually represents
Initial velocity (starting velocity)
Initial height (starting height)
Product Rule (Mnemonic)
Quotient Rule (Mnemonic)
LowDHi-HiDLow over the square of what's below
f'''(x) means the third derivative. We use tick marks to represent the level of all derivatives up to the third derivative. But how do we write the fourth derivative?
Chain Rule: d/dx[f(u)]=
Chain Rule: d/dx[f(g(x))]=
Never leave answers with _________ exponents
Never leave answers with _________ fractions
The chain rule states that if you take the derivative of the outside, and the inside is differentiable, then you have to multiply by the ________ of the __________
Explicit Form means that the equation is in terms of _____
Implicit Form means that there are x's and y's on the _______ _______ of an equation.
As you take a derivative of y with respect to x, you have to multiply the derivative by ________
In implicit differentiation, we multiply by dy/dx because of the _________ rule
d²y/dx² means to find the __________ ____________
Most of the problems in chapter 2 will use a combination of the power rule, along with these 3 rules.
Product Rule, Quotient Rule, Chain Rule
If a graph of an equation has a horizontal tangent line (slope of zero), then the graph of its derivative should cross the ___-_______ at that point
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https://www.nagwa.com/en/videos/893149734805/
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math
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Find the volume of the solid generated by rotating the region bounded by the curve 𝑦 equals negative 𝑥 squared plus two 𝑥 and the 𝑥-axis a complete revolution about the 𝑥-axis.
We recall that the formula we use to find the volume of a solid generated by rotating a region about an 𝑥-axis is the definite integral between 𝑎 and 𝑏 of 𝐴 of 𝑥 with respect to 𝑥, where 𝐴 of 𝑥 is a function which describes the area of the cross section of the volume at a given point. Now, sometimes a nicer formula to use is the definite integral between 𝑎 and 𝑏 of 𝜋 times 𝑦 squared with respect to 𝑥, where 𝑥 equals 𝑎 and 𝑥 equals 𝑏 are the vertical lines that bound our region. And this is the formula we’re going to apply in this question.
Now, to see what’s going on, let’s begin by sketching out the graph of 𝑦 equals negative 𝑥 squared plus two 𝑥. To find the 𝑥-intercept, we’ll set 𝑦 equal to zero and solve for 𝑥. So, that’s negative 𝑥 squared plus two 𝑥 equals zero. Let’s factor an 𝑥 such that 𝑥 times negative 𝑥 plus two equals zero. Now, of course, this statement can only be true if either 𝑥 is equal to zero or negative 𝑥 plus two is equal to zero. And if we solve the second equation by adding 𝑥 to both sides, we find the 𝑥 is equal to two. And so, those are the roots of our equation. They’re the points where the graph intersects the 𝑥-axis.
The equation itself is a quadratic with a negative coefficient of 𝑥 squared. That means it looks like an inverted parabola, as shown. And we’re going to be rotating this region 360 degrees about the 𝑥-axis. Since this region is bounded by the vertical lines 𝑥 equals zero and 𝑥 equals two, we can say the 𝑎 itself must be equal to zero and 𝑏 must be equal to two. So, the volume is the definite integral between zero and two of 𝜋 times 𝑦 squared. Now, 𝑦 is the equation negative 𝑥 squared plus two 𝑥. We can take a constant factor of 𝜋 outside of our integral. And then, the best way to integrate this is simply to distribute our parentheses. When we do, we find our integrand becomes 𝑥 to the fourth power minus four 𝑥 cubed plus four 𝑥 squared. So, let’s perform the integration.
We know that to integrate a polynomial term whose exponent is not equal to negative one, we add one to the exponent and then divide by that new value. This means the integral of 𝑥 to the fourth power is 𝑥 to the fifth power divided by five. When we integrate negative four 𝑥 cubed, we get negative four 𝑥 to the fourth power divided by four. Which simplifies do negative 𝑥 to the fourth power. And then, the integral of four 𝑥 squared is four 𝑥 cubed over three. Now, we need to evaluate this between the limits of zero and two. And so, this becomes 𝜋 times two to the fifth power over five minus two to the fourth power plus four times two cubed over three all minus zero.
This becomes 𝜋 times 32 over five minus 16 plus 32 over three. And then, we’re going to create a common denominator of 15. To do so, we multiply 32 over five by three over three. We write negative 16 as negative 16 over one and then multiply by 15. And we multiply 32 over three by five over five. This is 𝜋 times 96 over 15 minus 240 over 15 plus 160 over 15. Which simplifies fully to 16𝜋 over 15. And so, we can say that the volume of the solid generated by rotating the region bounded by the curve 𝑦 equals negative 𝑥 squared plus two 𝑥 and the 𝑥-axis 360 degrees about the 𝑥-axis is 16𝜋 over 15 cubic units.
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http://ideas.repec.org/a/eee/stapro/v71y2005i4p323-335.html
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math
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Chebyshev-type inequalities for scale mixtures
AbstractFor important classes of symmetrically distributed random variables X the smallest constants C[alpha] are computed on the right-hand side of Chebyshev's inequality P(X[greater-or-equal, slanted]t)[less-than-or-equals, slant]C[alpha]EX[alpha]/t[alpha]. For example if the distribution of X is a scale mixture of centered normal random variables, then the smallest C2=0.331... and, as [alpha]-->[infinity], the smallest C[alpha][downwards arrow]0 and .
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 71 (2005)
Issue (Month): 4 (March)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Thomas Sellke, 1996. "Generalized gauss-chebyshev inequalities for unimodal distributions," Metrika, Springer, vol. 43(1), pages 107-121, December.
- N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
If references are entirely missing, you can add them using this form.
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http://cooking.stackexchange.com/questions/tagged/jelly+jalapeno
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math
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Seasoned Advice Meta
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| 2,119 | 54 |
https://www.electronicsassignments.com/voltage-multipliers-12458
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math
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Diodes and capacitors can be connected in various configurations to produce filtered, rectified voltages that are integer multiples of the peak value of an input sine wave. The principle of operation of these circuits is similar to that of the clamping circuits discussed in Chapter 15. By using a transformer to change the amplitude of an ac voltage before it is applied to a voltage multiplier, a wide range of dc levels can be produced using this technique. One advantage of a voltage multip lier is that high voltages can be obtained without using a high-voltage transformer.
Half-Wave Voltage Doubler
A half-wave voltage doubler. When ViII first goes positive. diode DJ is forward biased and diode D, is reverse biased. Because the forward resistance of DJ is quite small, CJ charges rapidly to Vp (neglecting the diode drop), as shown in (b). During the ensuing negative half-cycle of Vin, DJ is reverse biased and D, is forward biased, as shown in (c). Consequently, C2 charges rapidly, with polarity shown. Neglecting the drop across D2, we can write Kirchhoff’s voltage law around the loop at the instant ViII reaches its negative peak, and obtain. During the next positive half-cycle of ViII, D2 is again reverse biased and the voltage across the output terminals remains at Ve2 == 2 VI’ volts. Note carefully the polarity of the output. If a load resistor is connected across C~,then C~ will discharge into the load during positive half-cycles of Vi,,, and will recharge to 2 \’ p Vults during negative half-cycles, creating the usual ripple waveform. The PIV raliJlg of each diode must be at least 2 Vp volts
Full-Wave Voltage Doubler
Figure 17-22(a) shows a full-wave voltage doubler. This circuit is the same as the full-wave bridge rectifier shown in Figure 17-6, with two of the diodes replaced by capacitors. When ViII is .positive, DI conducts and C, charges to VI’ volts. as shown in (b). When ViII is negative, D, conducts and C2 charges to Vp volts, with the polarity shown in (c). It is clear that the output voltage is then VC, +Vc1 = 2V/, volts. Since one or the other of the capacitors is charging during every half-cycle, the output is the same as that of a capacitor-Iiltered, full-wave rectifier. Note, however, that the effective filter capacitance is that of C, and C2 in series, which is less than either C, or C2• The PlY rating of each diode must be at least 2 VI’ volts.
Voltage Tripier and Quadrupler
By connecting additional diode-capacitor sections across the half-wave voltage doubler, output voltages equal to three and four times the input peak voltage can be obtained. The circuit is shown in Figure 17-23. When v'” first goes positive, C, charges to VI’ through forward-biased diode 01, On the ensuing negative half-cycle,C! charges through D! ami, as demonstrated earlier. the voltage a~ross C! equals 2 VI” During the next positive half-cycle, 0.1 is forward biased and C3 charges
the same voltage attained by C2: 2Vp volts. On the next neg-ative half-cycle, D2 and D4 are forward biased and C4 charges to 2Vp volts. As. shown in the figure, the • voltage across the combination of CI and C3 is 3Vp volts, and that across C2 and C4 is 4 VI’ volts. Additional stages can be added in an obvious way to obtain even greater multiples of VI” The PIV rating of each diode in the circuit must be at least 2Vp volts.
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CC-MAIN-2021-49
| 3,376 | 8 |
https://www.physicsforums.com/threads/singularity-problem.263161/
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math
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why lnZ is not isolated singularity?
Because you can't define ln(z) to be holomorphic in the disk after removing 0. It has multiple branches.
Questions on Poles
I am trying to do my homework on:
Integration form 0 to infinity of [( log x)^4 ]/[1+x^2] dx =
by first defining what is a branch cut and how it will fit into the above integrand.
Re: Questions on Poles
I don't recommend posting a brand new question onto an existing thread. Start a new one. While you're doing that figure out how to start the problem so you can post an attempt. Where are the poles?
How do I start the new threads?
The poles is x= +/- i
Go to the Calculus and Beyond forum and under Forum Tools you'll find start new thread.
Separate names with a comma.
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http://www.blackberryforums.com/buy-sell-trade/190854-wts-ic-verizon-curve-8330-a.html
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math
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Originally Posted by breakerfall
no thanks, just interested in the Curve...
is that a "no"?
It seems that this post was directed at my post of a Krave. I was asking the OP if he was interested in a trade for his Curve if there was any confusion.
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http://www.abovetopsecret.com/forum/thread142617/pg1
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math
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Time is generally measured as how long it takes something with constant velocity to travel a constant distance. Unfortunately, since velocity is also
relative to time, it is kind of hard to determine one independently of the other. For example, if I'm traveling at 60 mph, then in one hour I travel
60 miles. You could say that one hour is then the time it takes me to travel 60 miles. But if I somehow travel that distance in less (or greater)
time, then was it because I started accellerating/decellerating or because the time measured wasn't constant?
Generally speaking, light is used for this measure, and a second is the length of time it takes light to travel 186,000 miles in a vacuum. Of course,
this is still an interdependant calculation, because we can also look at it as 186,000 miles is the distance that light travels in one second (in a
vacuum.) In fact, if I remember correctly, that's how the figure for the speed of light came to be; it was measured against time, instead of time
being measured against it.
Another measure for time, mainly used by atomic clocks, is determining how long it takes an atom to vibrate a given number of times. That is more
appropriate in my opinion, but it's still somewhat interdependant. In order to determine the proper number of vibrations in a second, you have to
have your stopwatch there and count the number of vibrations that happen in one second.
While T_Jesus is right, mathematically speaking the speed of light is the physical limit on velocity, one thing I always found interesting with
relativity is you can use it to disprove that part of the theory. A bit of an explanation of the theory is in order here though.
Relative velocity is measured as one object moves in relation to another. An example Einstein himself used was this: you have two trains moving next
to each other on a platform, train A at 15 mph and train B at 20 mph. They're both moving in the same direction. From train A's perspective, train
B is pulling ahead at 5 mph. From train B's perspective, train A is moving backwards at 5 mph.
If they're moving in opposite directions at the same speeds (15 and 20), then if you look at one as being stationary, the other is moving away at 35
mph. This is using each train individually as a frame of reference. If you're standing on the platform and using the platform as your reference
frame, then each train is moving in it's direction at the speed stated.
The disproving of the speed limitation follows a similar pattern. If I'm on an extremely fast train moving at 60% the speed of light, and there's
another one moving away at 60% the speed of light, then in relation to each other we're traveling at 120% the speed of light, obviously faster than
the physical limitation.
(I can't remember if that has been disproven or is considered in the theory; if it has, then please forgive me.)
Warping space, in essence, is not FTL travel, because even though you are travelling a technically greater distance from point A to point B, you
aren't travelling the space in between. That said, you technically aren't travelling the "time" in between either. (I'm going off of
speculation here; no studying or research at all, just my own reasoning as flawed as it may be.) You could argue that it is time travel, because you
end up at one location the moment you left the other location.
For example, if you maintain a velocity of 60 mph, and you are planning on travelling a distance of 120 miles, it should take you 2 hours to get
there. You start at noon, you arrive at 2 pm. If you manage to bend space enough to elminate a 90 mile stretch in between, you only have a half hour
drive. You arrive 90 minutes sooner than you should have. You could reason that you travelled back in time 90 minutes from your original
destination. However, it isn't time travel in the sense that you would go back to a point in time before you left per se; don't get any ideas about
stopping Oswald (or the CIA, or Mafia, or whomever) by creating a Star Trek-esque warp drive.
Ok, now my head hurts too...I hope this made some kind of sense to someone
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https://rd.springer.com/book/10.1007%2F978-94-011-4679-1
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math
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About this book
The main part of the book is based on a one semester graduate course for students in mathematics. I have attempted to develop the theory of hyperbolic systems of differen tial equations in a systematic way, making as much use as possible ofgradient systems and their algebraic representation. However, despite the strong sim ilarities between the development of ideas here and that found in a Lie alge bras course this is not a book on Lie algebras. The order of presentation has been determined mainly by taking into account that algebraic representation and homomorphism correspondence with a full rank Lie algebra are the basic tools which require a detailed presentation. I am aware that the inclusion of the material on algebraic and homomorphism correspondence with a full rank Lie algebra is not standard in courses on the application of Lie algebras to hyperbolic equations. I think it should be. Moreover, the Lie algebraic structure plays an important role in integral representation for solutions of nonlinear control systems and stochastic differential equations yelding results that look quite different in their original setting. Finite-dimensional nonlin ear filters for stochastic differential equations and, say, decomposability of a nonlinear control system receive a common understanding in this framework.
Lie algebra algebra partial differential equation stochastic differential equation system
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CC-MAIN-2020-29
| 1,431 | 3 |
http://www.talkstats.com/threads/small-samples-multiple-predictors.72916/
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math
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Let us consider a song competition. There are 3 global criteria weighted A worth 40 points, B worth 30 points, and C worth 30 points, equaling a total of 100 points to determine the Winner. The 40-point criterion has 4 sub-dimensions, each with weightings of 5 pts, 15 ots, 15 pts, and 5 pts. The 2nd criterion has 3 sub-dimensions, with weightings of 15 pts, 10 pts, and 5 pts. The 3rd criterion has 3 sub-dimensions with weightings of 15 pts, 10 pts, and 5 pts. There are 30 competitors. There are 7 judges. Can regression analysis be used to determine which sub-dimension is the greatest predictor of their respective global criterion? Can it also be used to determine which global criterion is the greatest predictor of contestants' final scores? The concern is the limited data points with only 7 judges. And the uneven weightings of the 3 global criteria and their and sub dimensions. That is, 40 pts, 30 pts, and 30 points globally, then 5, 15, 15, 5 for the 2nt criterion and so on. Thanks in advance for your insight.
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CC-MAIN-2020-24
| 1,026 | 1 |
https://cedarwingsmagazine.com/articles/youtube-dividing-fractions
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math
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How do you divide fractions with answers?
The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.
Final thoughts on how to divide fractions
The easiest way to divide fractions is to follow three simple steps: Flip the divisor into a reciprocal. Change the division sign into a multiplication sign and multiply. Simplify if possible.
The rule for dividing fractions is you take the first fraction and multiply it by the reciprocal of the second fraction. Yes, you heard that right: to divide, you end up multiplying, but only after first flipping the second fraction around.
- The cross multiplication method. ...
- The inverse multiplication method.
The idea here is that we change a division to a multiplication by Keeping the first number as is, Changing the operation from multiplication to division, and Flipping the second number over (making its reciprocal). It's a way to avoid the big word “reciprocal”, just as “invert” and “upside down” have been used above!
The division of fractions means breaking down a fraction into further parts. For example, if you take half (1/2) of a pizza and you further divide it into 2 equal parts, then each portion will be 1/4th of the whole pizza. Mathematically, we can express this reasoning as 1/2 ÷ 2 = 1/4.
If you're just starting out with division, drawing a picture may help you to understand division problems better. First, draw the same number of boxes as the number for the divisor. Then move from box to box adding in a dot that represents 1 out of the total dividend. The number that you have in each box is the answer.
- Convert the mixed number to an improper fraction.
- Change the division to its inverse, multiplication, and change the divisor to its reciprocal.
- Multiply and simplify to find the quotient.
Students struggle with multiplying and dividing fractions because the operations don't result in the answer they expect. With whole numbers, students learned that division results in smaller numbers, and multiplication results in larger numbers. However, the opposite is typically true for fractions.
Remember that when you multiply or divide by a negative number in an inequality, you must flip the sign.
What is the easiest way to solve a fraction question?
All you have to do is subtract the smaller numerator from the larger numerator to solve the problem. For instance, to solve 6/8 - 2/8, all you do is take away 2 from 6. The answer is 4/8, which can be reduced to 1/2.
Step 1: Create a single fraction from both the denominator and the numerator. Step 2: Apply the division rule by multiplying the top of the fraction by the reciprocal of the bottom. Step 3: Simplify the fraction to its simplest terms.
In 5th grade, students should be able to understand fraction division and what it looks like in the real world. By 6th grade, students are expected to divide fractions by using the standard algorithm.
A formal introduction to fractions begins in Grade 3, where the Number and Operations—Fractions domain first appears in the mathematics standards. Students begin with the concept of unit fractions (3.
Let's look at an example: Priscilla bought cheese that weighs ¾ pounds. If she divides it into portions that are each 1/8 pound, how many portions can she make?
Our numerator was 8, so we divide that by the denominator, 25. Be Careful: always divide the denominator into the numerator and not the other way around. In other words, the numerator always goes inside the division box.
Dividing Mixed Numbers by Fractions
Convert the mixed number into an improper fraction. Multiply the first fraction with the reciprocal of the second. Finally, simplify the answer you get and convert it into a mixed number if required.
- Identify a common factor (a number that multiplies with another to make your given number) of both the numerator and denominator.
- Divide the numerator and the denominator by that same factor.
- You have a simplified fraction. Congratulations.
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CC-MAIN-2023-14
| 4,150 | 27 |
https://arteslonga.com/en/sold-out/886-50s-coffee-table-cocktail-party.html
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math
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50s Coffee Table, "Cocktail Party" - SOLD
En stock: 0
France and International delivery
50s coffee table with his printed formica tray, colorful "Cocktail Party" pattern. Design, color and black metal base are typical of the 50s.
Despite one or two minor scratches on the tray without gravity, this coffee table is in very good condition.
Width: 60 cm
Height: 40 cm
Depth: 47 cm
Weight: 10 kg
State: Excellent original condition
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CC-MAIN-2022-33
| 432 | 10 |
https://socratic.org/questions/56f258f911ef6b490ab9fdb7
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math
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The centripetal force acting on the truck as it rounds the curve must be 400N.
If the truck driver holds the wheel steady, then the path the truck takes around the corner is an arc, or segment of a circular path, basically a circle!
We can therefore calculate the centripetal force exerted on the (tires of the) truck (by the road) using equation 1).
Finding the amount (or magnitude) of the centripetal force simply requires substituting the numerical values for the physical quantities
But before we do that, let’s make sure that the units of the physical quantities
Ultimately, in the end, we want a force in newtons, N.
The velocity of the truck,
So let’s convert
So now, that our units are consistent, substituting
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CC-MAIN-2022-33
| 723 | 9 |
https://en-academic.com/dic.nsf/enwiki/8624882
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math
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- Proper velocity
In flat spacetime, proper-velocity is the ratio between distance traveled relative to a reference map-frame (used to define simultaneity) and
proper timeτ elapsed on the clocks of the traveling object. It equals the object's momentum p divided by its rest mass m, and is made up of the space-like components of the object's four-vectorvelocity. William Shurcliff's monograph [W. A. Shurcliff (1996) "Special relativity: the central ideas" (19 Appleton St, Cambridge MA 02138)] mentioned its early use in the Sears and Brehme text [Francis W. Sears & Robert W. Brehme (1968) "Introduction to the theory of relativity" (Addison-Wesley, NY) [http://catalog.loc.gov/webvoy.htm LCCN 680019344] , section 7-3] . Fraundorf has explored its pedagogical value [P. Fraundorf (1996) "A one-map two-clock approach to teaching relativity in introductory physics" ( [http://xxx.lanl.gov/abs/physics/9611011 arXiv:physics/9611011] )] while Ungar [A. A. Ungar (2006) " [http://ceta.mit.edu/pier/pier.php?paper=0512151 The relativistic proper-velocity transformation group] ", "Progress in Electromagnetics Research" 60, 85-94.] , Baylis [W. E. Baylis (1996) "Clifford (geometric) algebras with applications to physics" (Springer, NY) ISBN 0-8176-3868-7] and Hestenes [D. Hestenes (2003) " [http://modelingnts.la.asu.edu/html/overview.html Spacetime physics with geometric algebra] ", "Am. J. Phys." 71, 691-714] have examined its relevance from group theoryand geometric algebraperspectives. Proper-velocity is sometimes referred to as celerity [Bernard Jancewicz (1988) "Multivectors and Clifford algebra in electrodynamics" (World Scientific, NY) ISBN 9971502909] .
Unlike the more familiar coordinate velocity v, proper-velocity is useful for describing both super-relativistic and sub-relativistic motion. Like coordinate velocity and unlike four-vector velocity, it resides in the three-dimensional slice of spacetime defined by the map-frame. This makes it more useful for map-based (e.g. engineering) applications, and less useful for gaining coordinate-free insight. Proper-speed divided by lightspeed "c" is the
hyperbolic sineof rapidity η, just as the Lorentz factor γ is rapidity's hyperbolic cosine, and coordinate speed v over lightspeed is rapidity's hyperbolic tangent.
Imagine an object traveling through a region of space-time locally described by
Hermann Minkowski's flat-space metric equation ("c"dτ)2 = ("c"dt)2 - (dx)2. Here a reference map frame of yardsticks and synchronized clocks define map position x and map time t respectively, and the d preceding a coordinate means infinitesimal change. A bit of manipulation allows one to show that proper-velocity w = dx/dτ = γv where as usual coordinate velocity v = dx/dt. Thus finite w ensures that v is less than lightspeed "c". By grouping γ with v in the expression for relativistic momentum p, proper velocity also extends the Newtonian form of momentum as mass times velocity to high speeds without a need for relativistic mass[G. Oas (2005) "On the use of relativistic mass in various published works" ( [http://arxiv.org/abs/physics/0504111 arXiv:physics/0504111] )] .
Comparing proper velocities at high speed
Proper-velocity is useful for comparing the speed of objects with momentum per unit mass (w) greater than lightspeed "c". The coordinate speed of such objects is generally near lightspeed, whereas proper-velocity tells us how rapidly they are covering ground on "traveling-object clocks". This is important for example if, like some cosmic ray particles, the traveling objects have a finite lifetime. Proper velocity also clues us in to the object's momentum, which has no upper bound.
For example, a 45 GeV electron accelerated by the
Large Electron-Positron Collider(LEP) at Cern in 1989 would have had a Lorentz factor γ of about 88,000 (90 GeV divided by the electron rest mass of 511 keV). Its coordinate speed v would have been about sixty four trillionths shy of lightspeed "c" at 1 lightsecond per "map" second. On the other hand, its proper-speed would have been w = γv ~88,000 lightseconds per "traveler" second. By comparison the coordinate speed of a 250 GeV electron in the proposed International Linear Collider[B. Barish, N. Walker and H. Yamamoto, " [http://www.sciam.com/article.cfm?id=building-the-next-generation-collider Building the next generation collider] " "Scientific American" (Feb 2008) 54-59] (ILC) will remain near "c", while its proper-speed will significantly increase to ~489,000 lightseconds per traveler second.
Proper-velocity is also useful for comparing relative velocities along a line at high speed. In this case wAC = γABγBC(vAB+vBC) where A, B and C refer to different objects or frames of reference [This velocity-addition rule is easily derived from rapidities α and β, since Sinh [α+β] =Cosh [α] Cosh [β] (Tanh [α] +Tanh [β] ).] . For example wAC refers to the proper-speed of object A with respect to object C. Thus in calculating the relative proper-speed, Lorentz factors multiply when coordinate speeds add. Hence each of two electrons (A and C) in a head-on collision at 45 GeV in the lab frame (B) would see the other coming toward them at vAC ~"c" and wAC = 88,0002(1+1) ~1.55×1010 lightseconds per traveler second. Thus colliders can explore higher-speed collisions than can fixed-target accelerators.
Plotting "(γ-1) versus proper velocity" after multiplying the former by m"c"2 and the latter by mass m, for various values of m yields a family of kinetic energy versus momentum curves that includes most of the moving objects encountered in everyday life. Such plots can for example be used to show where lightspeed, Planck's constant, and Boltzmann energy kT figure in.
To illustrate, the figure at right with log-log axes shows objects with the same kinetic energy (horizontally related) that carry different amounts of momentum, as well as how the speed of a low-mass object compares (by vertical extrapolation) to the speed after perfectly inelastic collision with a large object at rest. Highly sloped lines (rise/run=2) mark contours of constant mass, while lines of unit slope mark contours of constant speed.
Objects that fit nicely on this plot are humans driving cars, dust particles in
Brownian motion, a spaceship in orbit around the sun, molecules at room temperature, a fighter jet at Mach 3, one radio wave photon, a person moving at one lightyear per traveler year, the pulse of a 1.8 MegaJoule LASER, a 250 GeV electron, and our observable universe with the blackbody kinetic energy expected of a single particle at 3 Kelvin.
Unidirectional acceleration via proper velocity
In flat spacetime,
proper accelerationis the three-vector acceleration experienced in the instantaneously-varying frame of an accelerated object [Edwin F. Taylor & John Archibald Wheeler (1966 1st ed. only) "Spacetime Physics" (W.H. Freeman, San Francisco) ISBN 0-7167-0336-X] . Its magnitude α is the frame-invariant magnitude of that object's four-acceleration. Proper-acceleration is also useful from the vantage point (or spacetime slice) of an observer. Not only may observers in all frames agree on its magnitude, but it also measures the extent to which an accelerating rocket "has its pedal to the metal".
In the unidirectional case i.e. when the object's acceleration is parallel or anti-parallel to its velocity in the spacetime slice of the observer, the "change in proper-velocity is the integral of proper acceleration over map-time" i.e. Δw=αΔt for constant α. At low speeds this reduces to the well-known relation between coordinate velocity and coordinate
accelerationtimes map-time, i.e. Δv=aΔt. For constant unidirectional proper-acceleration, similar relationships exist between rapidity η and elapsed proper-time Δτ, as well as between Lorentz factor γ and distance traveled Δx. To be specific:
:,where as noted above the various velocity parameters are related by:.
These equations describe some consequences of accelerated travel at high speed. For example, imagine a spaceship that can accelerate its passengers at "1-gee" (or 1.03 lightyears/year2) halfway to their destination, and then decelerate them at "1-gee" for the remaining half so as to provide earth-like artificial gravity from point A to point B over the shortest possible time. For a map-distance of ΔxAB, the first equation above predicts a mid-point Lorentz factor (up from its unit rest value) of γmid=1+α(ΔxAB/2)/c2. Hence the round-trip time on traveler clocks will be Δτ = 4(c/α)cosh-1 [γmid] , during which the time elapsed on map clocks will be Δt = 4(c/α)sinh [cosh-1 [γmid] .
This imagined spaceship could offer round trips to
Proxima Centaurilasting about 7.1 traveler years (~12 years on earth clocks), round trips to the Milky Way's central black holeof about 40 years (~54,000 years elapsed on earth clocks), and round trips to Andromeda Galaxylasting around 57 years (over 5 million years on earth clocks). Unfortunately, sustaining 1-gee acceleration for years is easier said than done.
Kinematics: for studying ways that position changes with time
Lorentz factor: γ=dt/dτ or kinetic energy over mc2
Rapidity: hyperbolic velocity angle in imaginary radians
Four-velocity: combining travel through time and space
Uniform Acceleration: holding coordinate acceleration fixed
Notes and References
* [http://www.eftaylor.com/download.html#special_relativity Excerpts from the first edition of "Spacetime Physics", and other resources posted by Edwin F. Taylor]
Wikimedia Foundation. 2010.
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https://analytik.co.uk/what-is-a-taylor-couette-fluid-flow-reactor/
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math
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What is a Taylor-Couette Fluid Flow Reactor?
What is Taylor-Couette Flow?
Taylor-Couette Flow is the flow of a viscous fluid when confined in the gap between two rotating cylinders; a round bar-type cylinder is inserted into a pipe-type cylinder. The resulting fluid flow is called Taylor-Couette flow.
The fluid flows in the rotating direction as the inner cylinder rotates, but there occurs a force for the fluids on the inner cylinder to go to the outer cylinder direction via a centrifugal force and a Coriolis force, so the fluid flow becomes gradually unstable as the rotation speed increases to create vortexes of ring pair array rotating regularly and in the counter directions along the axial direction.
A Taylor-Couette fluid flow can generate a turbulent flow by changing the rotational speed of the inner cylinder and is widely used to study the stability of a fluid.
For a viscous fluid, it was reported that a Taylor Vortex occurs in a domain larger than the critical Taylor number based on linear theory. The instability condition of a flow can be represented as a Taylor number (Ta), which is defined by a rotational direction Reynolds number and a reactor shape factor(d/R1) as follows:
Where d is the distance between two cylinders, R1 is the radius of the inner cylinder, ω1 is the rotational angular speed of the inner cylinder, and ν is the dynamic viscosity of the fluid.
A diagram illustrating Taylor-Couette Flow.
Laminar Continuous Taylor Reactors
Analytik provides Taylor-Couette Fluid Flow Reactors developed by South Korean manufacturer Laminar. Laminar’s patented chemical production technology commercialised Taylor Fluid Flow, developed by Couette in the early 1900s and analysed by Taylor in the mid-1900s, to develop the first Continuous Taylor Flow Reactor in 2010.
Laminar Continuous Taylor Reactors (LCTRs) have since been optimised for the manufacture of Li-ION batteries, development of nano materials and production of Graphene Oxide, and adopted by leading organisations across the globe.
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https://www.proprofs.com/discuss/q/864608/which-one-of-these-is-conclusion-the-baroncohen-experiment
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math
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Which one of these is a conclusion of the Baron-Cohen experiment?
A. The experiment supports the \
econstructive memory hypothesis\ B. There is evidence of deficit of subtle \mind reading\ amongst intelligent adults on the autistic spectrum C. The eye task is not a valid measure of theory of mind D. Option 4
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http://www.thefirearmsforum.com/showthread.php?mode=hybrid&t=99330
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math
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One Of The Many Things I Don't Know .....
Of the many things I don't know about a computer, How do you post something for which you have no link ?
I was sent something cute that I would like to post for the membership .... it's a series of clever household "tips" for which there are pictures included .
I can forward it, in e-mail, but I have no idea of how to post it on a board.
I'd like send it to someone that would post it for me, and/or, explain how to post it.
Thanks, in advance for the help !
Freedom .... Is Never Free !
We need Term Limits .... Send the "Professional Politicians" home .
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http://tfcourseworkftqs.musikevents.us/calculate-annual-break-even-point-in-dollar-sales-and-unit-sales-for-shop-48.html
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math
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This break-even formula calculator analyzes calculator analyzes your per-unit costs and revenues and your monthly overhead to determine your break-even sales. The calculation method for the break-even point of sales mix is to calculate the break-even point for sales break-even point in units and in dollars.
Answer to calculate the annual break-even point in unit sales and in dollar sales for shop 48 if 21, 900 pairs of shoes are sold. Unit sales to break even fixed expensesunit cm even point in dollar sales and in unit sales for shop 48 be the new break even point in dollar sales. Use our interactive calculator to find your business’s break-even point and of sales dollars left after the calculator to see your break-even point.
Use this formula to learn how to calculate a breakeven point to help make to the breakeven point if sales the 50,000 units necessary to break even. How do you calculate the break-even point in terms of sales the break-even point in sales dollars can be calculated by dividing a company's fixed expenses by the company's contribution.
The formulas used in the equation method for the calculation of break-even point in sales units and sales dollars are calculate break-even point in sales units.
This calculator will compute a company's break-even point in terms of both total sales and number of units sold, given the company's fixed costs, sales price per unit, and variable costs per.
Required: 1 calculate the annual break-even point in dollar sales and in unit sales for shop 48 2 prepare a cvp graph showing cost and revenue data for shop 48 from zero shoes up to. Know how to calculate your margin, markup and breakeven point to to calculate your margin, markup and breakeven sales to be made, (in dollars or units. Required: 1 calculate the annual break-even point in unit sales and in dollar sales for shop 48.
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http://www.chegg.com/homework-help/questions-and-answers/wave-on-a-rope-questions-1-how-does-the-speed-of-this-pulse-depend-on-the-hanging-mass-and-q3601221
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math
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Wave on a Rope questions.
1. How does the speed of this pulse depend on the hanging mass and mass density of the string?
2. What happens to the pulse when it reaches the end where a mass is located?
3. when a string is not fixed in position any longer, what happens to the pulse when it reaches the end?
3. when a wave is inverted at the end , it produce a single large wave that propagates to the right. Once it reaches the right side, it produces another large wave. Describe what should happen.
4. when doing part 3 again, but with a large amplitude pulse and a small amplitude pulse, what happens?
5. finally, What would you have to do to create a standing wave on a string?
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https://wiki-offline.jakearchibald.com/wiki/Distance-regular_graph
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math
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This article needs additional citations for verification. (June 2009)
In mathematics, a distance-regular graph is a regular graph such that for any two vertices v and w, the number of vertices at distance j from v and at distance k from w depends only upon j, k, and i = d(v, w).
Every distance-transitive graph is distance-regular. Indeed, distance-regular graphs were introduced as a combinatorial generalization of distance-transitive graphs, having the numerical regularity properties of the latter without necessarily having a large automorphism group.
It turns out that a graph of diameter is distance-regular if and only if there is an array of integers such that for all , gives the number of neighbours of at distance from and gives the number of neighbours of at distance from for any pair of vertices and at distance on . The array of integers characterizing a distance-regular graph is known as its intersection array.
Cospectral distance-regular graphs
A pair of connected distance-regular graphs are cospectral if and only if they have the same intersection array.
A distance-regular graph is disconnected if and only if it is a disjoint union of cospectral distance-regular graphs.
Suppose is a connected distance-regular graph of valency with intersection array . For all : let denote the -regular graph with adjacency matrix formed by relating pairs of vertices on at distance , and let denote the number of neighbours of at distance from for any pair of vertices and at distance on .
- for all .
- and .
- for any eigenvalue multiplicity of , unless is a complete multipartite graph.
- for any eigenvalue multiplicity of , unless is a cycle graph or a complete multipartite graph.
- if is a simple eigenvalue of .
- has distinct eigenvalues.
If is strongly regular, then and .
Some first examples of distance-regular graphs include:
- The complete graphs.
- The cycles graphs.
- The odd graphs.
- The Moore graphs.
- The collinearity graph of a regular near polygon.
- The Wells graph and the Sylvester graph.
- Strongly regular graphs of diameter .
Classification of distance-regular graphs
There are only finitely many distinct connected distance-regular graphs of any given valency .
Similarly, there are only finitely many distinct connected distance-regular graphs with any given eigenvalue multiplicity (with the exception of the complete multipartite graphs).
Cubic distance-regular graphs
The cubic distance-regular graphs have been completely classified.
The 13 distinct cubic distance-regular graphs are K4 (or Tetrahedral graph), K3,3, the Petersen graph, the Cubical graph, the Heawood graph, the Pappus graph, the Coxeter graph, the Tutte–Coxeter graph, the Dodecahedral graph, the Desargues graph, Tutte 12-cage, the Biggs–Smith graph, and the Foster graph.
- Bang, S.; Dubickas, A.; Koolen, J. H.; Moulton, V. (2015-01-10). "There are only finitely many distance-regular graphs of fixed valency greater than two". Advances in Mathematics. 269 (Supplement C): 1–55. arXiv:0909.5253. doi:10.1016/j.aim.2014.09.025. S2CID 18869283.
- Godsil, C. D. (1988-12-01). "Bounding the diameter of distance-regular graphs". Combinatorica. 8 (4): 333–343. doi:10.1007/BF02189090. ISSN 0209-9683. S2CID 206813795.
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CC-MAIN-2021-25
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https://martialarts.stackexchange.com/questions/8600/target-pad-design
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math
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Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Why do some handheld target pads have a double-layer design? I remember using a single layer pad when I was a kid. Since then, the double layer design has been introduced.
At best I can tell, it makes a louder noise when you hit it, but that's it.
8 days ago
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https://les-grizzlys-catalans.org/is-power-a-scalar-or-vector/
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math
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You are watching: Is power a scalar or vector
Power on its own is defined as being the rate of energy transfer, and it has no additional information as to its direction, so it is a scalar. However, there is a vectorial quantity which is related to power, known as the Poynting vector.
Given say, an electric field $mathbfE$ and magnetic field $mathbf B$, the Poynting vector is defined as,
$$mathbf S = frac1mu_0mathbf E imes mathbf B$$
which is the power in the direction of $mathbf S$, per unit area. Thus, if we want to know the power going through a surface $A$, it would be,
$$P = iint_A mathbf S , cdot mathrm dmathbf A.$$
Thus, power on its own is a scalar quantity, but we do have a notion of direction for power which is encoded in the Poynting vector, or analogues of it for other phenomena.
Improve this answer
answered Oct 4 "17 at 15:14
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Whether a quantity is a scalar or vector or higher-ranked tensor actually depends on how they are used to model a physical process and how they need to transform under coordinate transformations.
Vectors have certain transformation properties, most notably rotational, which are different from scalars, and tensors have transformation properties which are different from vectors, etc.
When introducing les-grizzlys-catalans.org to beginners, the ideas of vectors and scalars are simplified, and they seem like arbitrary assignments to the students. At higher levels of les-grizzlys-catalans.org, the concepts of rotation are brought in and are used to explain why a velocity is a vector, but mass is not, and so on. At even higher levels, tensors are introduced, and in relativity the electromagnetic field, previously modeled as a couple of vectors, $vecE$ and $vecB$, is presented in the form of a tensor, again due to transformation properties using the tools of mathematics.
Another conceptual construct is the 4-vector which has certain attractive transformation properties for modeling physical processes and doing calculations.
See more: How To Sneak Someone Into Your House ? How Can I Sneak My Boyfriend Into My House
Power and work are some of those modeled, conceptual, important quantities which, in lower level les-grizzlys-catalans.org can be treated as scalars.
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https://www.jiskha.com/display.cgi?id=1222202914
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math
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posted by amanda .
For the men age 18 and over the avg height was 69 inches with an SD of 3 inches and avg weight was 190 lbs with an SD of 42 pounds. the r value is around 0.41. Estimate the average weight of the men whose heights were 66in, 24 in, and 0in.
Let's gather the data:
Height (x): mean = 69, sd = 3
Weight (y): mean = 190, sd = 42
Correlation: r = 0.41
Regression equation is in this format:
predicted y = a + bx
...where a = intercept and b = slope.
To find the equation, you need to substitute the information given in the problem into a workable formula:
predicted y = (rSy/Sx)X - (rSy/Sx)xbar + ybar
...where r = correlation, Sy = sd of y, Sx = sd of x, and X is the variable in 'a + bx' equation.
Note: xbar = mean of x; ybar = mean of y.
Therefore: predicted y = [(0.41)(42)/(3)]X - [(0.41)(42)/(3)]69 + 190 = 5.74X - 206.06
predicted y = -206.06 + 5.74x
Check the math, then substitute the weights given for x, solving for predicted y.
I hope this will help.
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http://electricaldarwaza.com/electrical-technology/main-features-of-electric-current-2/
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math
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In our house there are several electrical and electronic devices, which require different electrical quantities such as electrical voltage, electrical current, electrical resistance and electrical power. In this article we decided to approach one of the main electrical quantities, which is the electric current, in order to show the main characteristics of the electric current.
What is Electric Current?
All substances, gaseous, liquid or solid, are made up of small particles invisible to the human eye, called atoms. The atom is basically divided into two parts, which is the nucleus and the electrosphere. In the nucleus is where protons and neutrons are located, the proton has a positive charge and the neutron has no electrical charge. In the electrosphere is where the electrons that have negative shits are located.
In the existing electrical conductor’s free electrons that are in constant disordered movement. For free electrons to move in an orderly manner in electrical conductors, it is necessary to have a force that drives free electrons, and this force is called electrical voltage.
The force caused by the electrical voltage causes the free electrons to move in an orderly fashion, thus forming an electron current that is called an electric current, represented by the letter (I).
The intensity of the electric current is determined by the ratio between the amount of electrical charges, which cross a determined section of a conductor, over a period of time. The unit of measurement given for the intensity of the electric current by the international system of units (SI) is the amp, in honor of the French scientist, André-marie Ampère (1775 – 1836), to represent the electric current we use the letter (A) as symbol. ).
Types of Electric Current
There are two types of electric current, direct current and alternating current. Direct current (DC or DC) is an ordered flow of free electrons in the same direction, remaining constant over time and has defined roles, that is, positive and negative poles, and this type of electrical current is obtained from the battery, battery, power supplies, charger etc.
Alternating electric current (AC or AC – from English alternating current), is the ordered flow of free electrons in a varied direction over time and has no poles defined as indirec current, varying between phase and neutral means to be present in hydroelectric plants, electrical outlets, substations, etc.
Electric Current Direction
Before studying the structure of atoms there was already a definition for electric current as being the direction of the flow of positive charges, so the charges move from the positive pole to the negative pole.
At the beginning of the history of electricity, because they were not aware of the structure of atoms, they did not know that in solid conductors the positive charges are strongly linked to the nuclei of the atoms, therefore, in solid conductors there can be no positive charge flow.
However, when subatomic physics discovered this fact, the definition for electric current as a flow of positive charges was already widely used in calculations and representations for circuit analysis, so this sense is still used today and is called the conventional current sense. electrical. Thus two directions were defined for the electric current, that is, the real sense and the conventional sense, where the real sense is the flow of electrons from the negative pole to the positive pole and the conventional sense is used in calculations for circuit analysis, being that in this case the direction of the electric current goes from the positive pole to the negative pole of the source.
Electric Current in each type of electrical circuit
The electrical circuit is a closed path through which the electric current flows, there are basically three types of circuit, which are: series, parallel and mixed circuit . The electrical current behaves in different ways in each type of electrical circuit, whereas in series circuits the electrical current is the same at all points. In parallel, the electric current is divided between the meshes, and may have different values of electric current, depending on the point of analysis. In the mixed circuit the electric current behaves in both ways, depending on the analyzed grid.
In order to carry out the analysis and calculations on the circuits, laws and formulas were developed over time, for example, ohm’s law , first kirchhoff’s law and current divider.
Ohm’s law is one of the most applied laws in electrical calculations. Ohms’ law is the basis for electrical calculations and involves four electrical quantities, which are: electrical voltage, electrical current, electrical resistance and electrical power . Ohm’s law is very simple, when we have the value of two of these quantities it is possible to find the value of the third variable, for that it is enough to use the appropriate formula, in the case of the electric current we have three formulas that can be used to obtain the value of electric current.
Kirchhoff’s first law
Kirchhoff’s laws are fundamental to perform series, parallel or mixed circuit analysis, as they are directly related to electrical current. Kirchhoff’s first law, also known as the law of currents or the law of nodes, is related to the electric current in a node. Kirchhoff’s first law says that the result of the sum of the electrical currents in a node is always equal to zero, so the node does not accumulate charge.
The node is a point where the current divides having two or more paths to travel in the circuit and the sum of all currents entering a node is equal to the sum of all currents leaving the node.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703531429.49/warc/CC-MAIN-20210122210653-20210123000653-00436.warc.gz
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CC-MAIN-2021-04
| 5,695 | 20 |
https://www.powerframeworks.com/frame-1387
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math
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Part of series: DD004 – Data-Driven Chart 004 Subdivided Bar Charts
This template has two 100% subdivided bar charts, with only one set of labels on the left-hand side of the vertical baseline for the left-hand chart. Use this template if the labels are the same for each of the two charts. Use v10 if the labels are different on both bar charts.
The labels to the left of the vertical baseline are left and center aligned. They are outside the graphing datasheet to provide more control over size, line breaks, and alignment.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347435238.60/warc/CC-MAIN-20200603144014-20200603174014-00114.warc.gz
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CC-MAIN-2020-24
| 528 | 3 |
https://space.stackexchange.com/questions/27672/russian-soyuz-ms-09-launch-back-and-forth-rotation-of-the-second-stage-along
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math
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In the ISS Expedition 56-57 Launch of Russian Soyuz MS-09, in the first view from the external camera at around 3:30, an obvious back and forth rotation (along the length axis) of the rocket can be seen against the earth background. Its amplitude diminishes until it is no longer visible around 4:30.
Is the rocket precessing? Why? And why does this precession decrease? Active correction?
Here is a video where you can see it from 3:15. I estimate fhe frequency of the phenomenon to be 0.5-0.7 Hz.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989637.86/warc/CC-MAIN-20210518125638-20210518155638-00186.warc.gz
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CC-MAIN-2021-21
| 498 | 3 |
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