Sucient Conditions Research Articles

Regularity Of Cubic Graph With Application

A cubic graph is a generalized structure of a fuzzy graph that gives moreprecision, flexibility and compatibility to a system when compared with systems thatare designed using fuzzy graphs. In this paper, some properties of an edge regularcubic graph are given. Particularly, strongly regular, edge regular and bi-regularcubic graphs are defined and the necessary and sucient condition for a cubic graphto be strongly regular is studied. Likewise, we have introduced a partially edgeregular cubic graph and fully edge regular cubic graph with suitable illustrations.Finally, we gave an application of cubic digraph in travel time.

INEXTENSIBLE FLOWS OF CURVES ACCORDING TO SABBAN FRAME IN GALILEAN SPACE G3

In this paper inextensible ows of curves in 3-dimensional Galilean space is researched. Firstly Sabban frame is dened in 3-dimensional Galilean space, then necessary and sucient conditions for inextensible ows of curves with Sabban frame in 3-dimensional Galilean space are given. Also inextensible curve ow are expressed as a partial dierential equation involving geodesic curvature according to this frame.

The extended SSVI volatility surface

We extend Gatheral and Jacquier SSVI volatility surface parameterisation by making the correlation maturity-dependent, obtaining necessary and sucient conditions for no calendar-spread arbitrage. Parametric families for the correlation are provided for which those conditions are explicit. This extension of SSVI typically increases the calibration accuracy for short maturities, and may also be more robust in stressed market conditions.

Existence and stability of traveling wavefronts for discrete three species competitive-cooperative systems.

The purpose of this work is to investigate the existence and stability of traveling wavefronts for competitive-cooperative systems with three species. The existence result can be derived by using the technique of monotone method with the help of a pair of explicit supersolution and subsolution. Moreover, some su cient conditions ensure the linear determinacy for the minimal speed is given. Then, applying the weighted energy method, we prove that the traveling wavefronts are asymptotically stable in the weighted Banach spaces provided that the initial perturbations of the traveling wavefronts also belong to the same spaces.

The survival analysis of a stochastic Lotka-Volterra competition model with a coexistence equilibrium.

In this paper, we propose and analyze a two-species Lotka-Volterra competition model with random perturbations that relate to the inter-specific competition rates and the coexistence equilibrium of the corresponding deterministic system. The stochasticity in inter-specific competition (between species) is more important than that in intra-specific competition (within species). We pose two assumptions and then obtain su cient conditions for coexistence and for competitive exclusion respectively, and find that small random perturbations will not destroy the dynamic behaviors of the corresponding deterministic system. Moreover, if one species goes extinct, the convergence rate to zero is obtained by investigating the Lyapunov exponent. Finally, we provide several numerical examples to illustrate our mathematical results.

The Extended SSVI Volatility Surface

We extend Gatheral and Jacquier SSVI volatility surface parameterisation by making the correlation maturity-dependent, obtaining necessary and sucient conditions for no calendar-spread arbitrage. Parametric families for the correlation are provided for which those conditions are explicit. This extension of SSVI typically increases the calibration accuracy for short maturities, and may also be more robust in stressed market conditions.

Transparency and Fairness in School Choice Mechanisms

This article explores the impact of procedural information on the behavior of applicants under two of the most commonly used school admissions procedures: the Gale-Shapley mechanism and the Boston mechanism. In a lab experiment, I compare the impact of information about the mechanism, information about individually optimal application strategies, and information about both. I find that strategic and full information increase truth-telling and stability under the Gale-Shapley mechanism. Under the Boston mechanism, however, the adoption of equilibrium strategies remains unaffected. Contrary to prevailing assumptions in matching theory, I show that the Boston mechanism improves perceived fairness. These results underscore the importance of procedural information and suggest that eliminating justified envy may not be a sucient condition of fairness.

Blow up and globality of solutions for a nonautonomous semilinear heat equation with Dirichlet condition

In this paper we prove the local existence of a nonnegative mild solution for a nonautonomous semilinear heat equation with Dirichlet condition, and give sucient conditions for the globality and for the blow up infinite time of the mild solution. Our approach for the global existence goes back to the Weissler's technique and for the nite time blow up we uses the intrinsic ultracontractivity property of the semigroup generated by the diffusion operator.

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The main asymptotic property of the continuous stochastic approximation procedure, namely the convergence to the Ornstein-Uhlenbeck process, is considered. The regression function of the procedure depends on a uniformly ergonomic Markov process, which describes the external inuence in the form of switches. To obtain sucient conditions for the convergence of the procedure, we use ergodic properties of the generating Markov process generator, the existence of a stationary distribution of this process, and the existence of the potential for a generating Markov process generator. The stochastic approximation procedure, as a random process, is constructed in the form of a dierential equation in the xed state of a Markov process with a corresponding generator of the equation. Asymptoticity over time is achieved by using a small parameter that normalizes time. This made it possible to obtain a normalized stochastic approximation procedure and its dierential representation. The generator of the obtained dierential equation is used to construct a generator of a two-component Markov process, which consists of a procedure and a switching process. The singular representation of the last generator by a small parameter makes it possible to solve the singular perturbation problem and determine the form of the limited generator. Such form denes the representation of a limited process as the Ornstein-Uhlenbeck diusion process. Note that the convergence to the limited process is weak, which follows from the Koroliuk's theorem. The conditions for the existence of the Lyapunov function for the dynamic procedure, which is averaged by the stationary distribution of the Markov process, are important. Additional conditions on the Lyapunov function make it possible to establish the boundedness of the residual terms of the solution of a singular perturbation. The one-dimensional case of the procedure can be expanded to multidimensional with the corresponding complication of calculations of the components of the limited generator. The work summarizes the studies of Nevelson and Khasminsky in the case of a direct inuence of the Markov process on the regression function.

Inference on Directionally Differentiable Functions

This paper studies an asymptotic framework for conducting inference on parameters of the form ( 0), where is a known directionally dierentiable function and 0 is estimated by ^ n. In these settings, the asymptotic distribution of the plug-in estimator ( ^ n) can be readily derived employing existing extensions to the Delta method. We show, however, that the \standard bootstrap is only consistent under overly stringent conditions { in particular we establish that dierentiability of is a necessary and sucient condition for bootstrap consistency whenever the limiting distribution of ^ n is Gaussian. An alternative resampling scheme is proposed which remains consistent when the bootstrap fails, and is shown to provide local size control under restrictions on the directional derivative of . We illustrate the utility of our results by developing a test of whether a Hilbert space valued parameter belongs to a convex set { a setting that includes moment inequality problems and certain tests of shape restrictions as special cases.

Some Results on Projective Curvature Tensor of Nearly Cosymplectic Manifold

In the nearly cosymplectic manifold, dened a tensor of type (4,0), it's called a projective curvature tensor. In this article we discuss an interesting question; what the geometric meaning of this tensor when it's act on nearly cosymplectic manifold? The answer of this question leads to get an application on Einstein space. In particular, the necessary and sucient conditions that a projective tensor is vanishes are found.

Locally Conformal Almost Cosymplectic Manifold of Φ-holomorphic Sectional Conharmonic Curvature Tensor

The aim of the present paper is to study the geometry of locally conformal almost cosymplectic manifold of Φ-holomorphic sectional conharmonic curvature tensor. In particular, the necessaryand sucient conditions in which that locally conformal almost cosymplectic manifold is a manifold of point constant Φ-holomorphic sectional conharmonic curvature tensor have been found. The relation between the mentioned manifold and the Einstein manifold is determined.

On Bäcklund and Ribaucour transformations for hyperbolic linear Weingarten surfaces

We consider Bäcklund transformations for hyperbolic linear Weingarten surfaces in Euclidean 3-space. The composition of these transformations is obtained in the Permutability Theorem that generates a 4-parameter family of surfaces of the same type. Since a Ribaucour transformation of a hyperbolic linear Weingarten surface also gives a 4-parameter family of such surfaces, one has the following natural question. Are these two methods equivalent, as it occurs with surfaces of constant positive Gaussian curvature or constant mean curvature? By obtaining necessary and sucient conditions for the surfaces given by the two procedures to be congruent.The analytic interpretation of the geometric results is given in terms of solutions of the sine-Gordon equation.

Quantitative homogenization of degenerate random environments

We study discrete linear divergence-form operators with random coecients, also known as the random conductance model. We assume that the conductances are bounded, independent and stationary; the law of a conductance may depend on the orientation of the associated edge. We give a simple necessary and sucient condition for the relaxation of the environment seen by the particle to be diusive, in the sense of every polynomial moment. As a consequence, we derive polynomial moment estimates on the corrector. MSC 2010: 35B27, 35K65, 60K37.

The representation type of the character ring

Let R(G) be the character ring of a nite group G. We consider the question whether the representation type of R(G) is nite or in nite. We show that if R(G) is representation- nite, then exp(G) is cube-free and the Sylow subgroups of G are cyclic, elementary-abelian, or nonabelian of order 8. Moreover, we give further necessary as well as some sucient conditions on the structure of G for the niteness of the representation type of R(G).

Study of Multivalent Spirallike Bazilevic Functions

In this paper, we introduce certain new subclasses of multivalent spirallike Bazilevicfunctions by using the concept of k-uniformly starlikness and k-uniformly convexity. We proveinclusion relations, su cient condition and Fekete-Szego inequality for these classes of functions.Convolution properties for these classes are also discussed.

Collective Choice Rules on Convex Restricted Domains

We consider restricted domains where each individual has a domain of preferences containing some partial order. This partial order might differ for different individuals. Necessary and sucient conditions are formulated under which these restricted domains admit unanimous, strategy-proof and, non-dictatorial choice rules.

Existence and uniqueness of monotone positive solutions for a third-order three-point boundary value problem

In this work we study a third-order three-point boundary-value problem (BVP). We derive sucient conditions that guarantee the positivity of the solution of the corresponding linear BVP Then, based on the classi- cal Guo-Krasnosel'skii's fixed point theorem, we obtain positive solutions to the nonlinear BVP. Additional hypotheses guarantee the uniqueness of the solution.

Induction, Bounding, Weak Combinatorial Principles, and the Homogeneous Model Theorem

Goncharov and Peretyat’kin independently gave necessary and su cient conditions for when a set of types of a complete theory T is the type spectrum of some homogeneous model of T . Their result can be stated as a principle of second order arithmetic, which we call the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states that every complete atomic theory has an atomic model. We show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense. We do the same for an analogous result of Peretyat’kin giving necessary and su cient conditions for when a set of types is the type spectrum of some model. Along the way, we analyze a number of related principles. Some of these turn out to fall into well-known reverse mathematical classes, such as ACA0, I⌃2, and B⌃2. Others, however, exhibit complex interactions with first order induction and bounding principles. In particular, we isolate several principles that are provable from I⌃2, are (more than) arithmetically conservative over RCA0, and imply I⌃ 0 2 over B⌃2. In an attempt to capture the combinatorics of this class of principles, we introduce the principle ⇧1GA, as well as its generalization ⇧ 0 n GA, which is conservative over RCA0 and equivalent to I⌃0 n+1 over B⌃ 0 n+1. Received by the editor July 22, 2015. 2010 Mathematics Subject Classification. Primary 03B30; Secondary 03C07, 03C15, 03C50, 03C57, 03D45, 03F30, 03F35. Hirschfeldt was partially supported by the National Science Foundation of the United States, grants DMS-0801033 and DMS-1101458. Lange was partially supported by NSF Grants DMS-0802961 and DMS-1100604. Shore was partially supported by NSF Grants DMS-0554855, DMS-0852811, and DMS1161175, John Templeton Foundation Grant 13408, and a short term visiting position at the University of Chicago as part of the Mathematics Department’s visitor program. v CHAPTER

Shannon Entropy And Tracking Dynamic Systems Over Noisy Channels

This paper is concerned with the estimation of state trajectory of linear discrete timedynamic systems subject to parametric uncertainty over the compound erasure channelthat uses feedback channel intermittently. For this combined system and channel,using the data processing inequality and a robust version of the Shannon lower bound,a necessary condition on channel capacity for estimation of state trajectory at thereceiver giving almost sure asymptotically zero estimation error is presented. Then,an estimation technique over the compound erasure channel that includes an encoder,decoder and a sucient condition under which the estimation error at the receiveris asymptotically zero almost surely is presented. This leads to the conclusion thatover the compound erasure channel, a condition on Shannon capacity in terms ofthe rate of expansion of the Shannon entropy is a necessary and sucient conditionfor estimation with uniform almost sure asymptotically zero estimation error. Thesatisfactory performance of the proposed technique is illustrated using simulation.