Search

Recent work by Volz (J Math Biol 56:293-310, 2008) has shown how to calculate the growth and eventual decay of an SIR epidemic on a static random network, assuming infection and recovery each happen at constant rates. This calculation allows us to account for effects due to heterogeneity and finiteness of degree that are neglected in the standard mass-action SIR equations. In this note we offer an alternate derivation which arrives at a simpler-though equivalent-system of governing equations to that of Volz. This new derivation is more closely connected to the underlying physical processes, and the resulting equations are of comparable complexity to the mass-action SIR equations. We further show that earlier derivations of the final size of epidemics on networks can be reproduced using the same approach, thereby providing a common framework for calculating both the dynamics and the final size of an epidemic spreading on a random network. Under appropriate assumptions these equations reduce to the standard SIR equations, and we are able to estimate the magnitude of the error introduced by assuming the SIR equations. [ABSTRACT FROM AUTHOR]

This paper is concerned with time-asymptotic nonlinear stability of rarefaction waves to the Cauchy problem for one-dimensional compressible non-isentropic magnetohydrodynamics (MHD) equations (including its isentropic case), which describe the motion of a conducting fluid in a magnetic field. Through some elaborate and rigorous mathematical analysis, we can construct the rarefaction waves v r , u r , θ r , b r (x / t) where magnetic component b r x / t is a nontrivial profile, namely a non-constant function. Then the solution of the compressible MHD equations is proved to tend towards the rarefaction waves time-asymptotically under small initial perturbations and weak wave strength, and also under a technical assumption that the parameter β = v + b + is bounded by a specific constant. The proof of the main result is based on elementary L 2 energy methods. [ABSTRACT FROM AUTHOR]

The A ^ 2 n (2) -hierarchy can be constructed from a splitting of the Kac–Moody algebra of type A ^ 2 n (1) by an involution. By choosing certain cross section of the gauge action, we obtain the A ^ 2 n (2) -KdV hierarchy. They are the equations for geometric invariants of isotropic curve flows of type A, which gives a geometric interpretation of the soliton hierarchy. In this paper, we construct Darboux and Bäcklund transformations for the A ^ 2 n (2) -hierarchy, and use it the construct Darboux transformations for the A ^ 2 n (2) -KdV hierarchy and isotropic curve flows of type A. Moreover, explicit soliton solutions for these hierarchies are given. [ABSTRACT FROM AUTHOR]

In this paper, we study the L p -boundedness of the commutator [ b , S R δ (H) ] (f) = b S R δ (H) f - S R δ (H) (b f) of a BMO function b and the Bochner–Riesz means S R δ (H) for Hermite operator H = - Δ + | x | 2 on R n , n ≥ 2 . We show that if δ > δ (q) = n (1 / q - 1 / 2) - 1 / 2 , the commutator [ b , S R δ (H) ] is bounded on L p (R n) whenever q < p < q ′ and 1 ≤ q ≤ 2 n / (n + 2) . [ABSTRACT FROM AUTHOR]

In this paper, finite element methods for the problems of wave propagation in a fluid-saturated porous medium are discussed. The medium is composed of a porous elastic solid (soil, rock, etc.) saturated by a compressible viscous fluid (oil, water, etc.), and the fluid may flow relatively to the solid. Biot's lowfrequency dynamic equations are chosen to describe the problems mentioned above, with stress-given boundary conditions, ABGs (Absorbing Boundary Conditions) on artificial boundaries and conditions on interfaces between the fluid-saturated porous medium and elastic solids. In the paper, a new kind of discrete ABCs is presented, and a discrete-time Galerkin method are utilized for obtaining approximate solutions. The numerical results show that they both are effective. Two dilatational waves (fast wave P1 and slow wave P2) and one rotational wave (S wave) are clearly visible in the figures of computational results, which coincide with theoretical analysis very well. [ABSTRACT FROM AUTHOR]

In this paper, we describe the range of the Lp-norm of a function under fixed Lp-norms with two other different exponents p and under a natural multiplicative restriction of the type of the Muckenhoupt condition. Particular cases of such results are simple inequalities as the interpolation inequality between two Lp-norms as well as such nontrivial inequalities as the Gehring inequality or the reverse Hölder inequality for Mackenhoupt weights. The basic method of our paper is the search for the exact Bellman function of the corresponding extremal problem. Bibliography: 5 [ABSTRACT FROM AUTHOR]

In this paper, we consider a Cauchy problem for an elliptic equation in a plane domain. The problem is ill-posed. Using the method of quasi-reversibility, an approximation to the exact solution is given. Using Carleman's inequatily, we derive a sharp error estimate. [ABSTRACT FROM AUTHOR]

In our original paper [4], Theorem 2.1 of [2], that we quoted, was not properly proved. This was done by Lee-Louboutin [3]. The gap doesn't affect the final result of the paper. [ABSTRACT FROM AUTHOR]

This paper presents new approximation bounds for trilinear and biquadratic optimization problems over nonconvex constraints. We first consider the partial semidefinite relaxation of the original problem, and show that there is a bounded approximation solution to it. This will be achieved by determining the diameters of certain convex bodies. We then show that there is also a bounded approximation solution to the original problem via extracting the approximation solution of its semidefinite relaxation. Under some conditions, the approximation bounds obtained in this paper improve those in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate how the initial value belonging to spaces $W_{\sigma}(\mathbb{R}^{N})$ ( $0<\sigma

We are concerned with the following class of equations with exponential nonlinearities: which is related to the Tzitzéica equation. Here $$h_1, h_2$$ are two smooth positive functions. The purpose of the paper is to initiate the analytical study of the above equation and to give a quite complete picture both for what concerns the blow-up phenomena and the existence issue. In the first part of the paper we provide a quantization of local blow-up masses associated to a blowing-up sequence of solutions. Next we exclude the presence of blow-up points on the boundary under the Dirichlet boundary conditions. In the second part of the paper we consider the Tzitzéica equation on compact surfaces: we start by proving a sharp Moser-Trudinger inequality related to this problem. Finally, we give a general existence result. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non- convexities: integer variables and non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-and-project methodology. In particular, we propose new methods for generating valid inequalities from the equation Y = x x T. We use the non-convex constraint $${ Y - x x^T \preccurlyeq 0}$$ to derive disjunctions of two types. The first ones are directly derived from the eigenvectors of the matrix Y − x x T with positive eigenvalues, the second type of disjunctions are obtained by combining several eigenvectors in order to minimize the width of the disjunction. We also use the convex SDP constraint $${ Y - x x^T \succcurlyeq 0}$$ to derive convex quadratic cuts, and we combine both approaches in a cutting plane algorithm. We present computational results to illustrate our findings. [ABSTRACT FROM AUTHOR]

We seek the optimal boundary control of vibrations of a spherical layer in the spherically symmetric case. This paper continues the series of papers by V.A. Il’in and his students and, unlike the previous papers, uses a more general control optimality criterion. We obtain closed formulas for the controls; these formulas are consistent with Il’in’s earlier results. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, a discontinuous Galerkin least-squares finite element method is developed for singularly perturbed reaction-diffusion problems with discontinuous coefficients and boundary singularities by recasting the second-order elliptic equations as a system of first-order equations. In a companion paper (Lin in SIAM J Numer Anal 47:89–108, 2008) a similar method has been developed for problems with continuous data and shown to be well-posed, uniformly convergent, and optimal in convergence rate. In this paper the method is modified to take care of conditions that arise at interfaces and boundary singularities. Coercivity and uniform error estimates for the finite element approximation are established in an appropriately scaled norm. Numerical examples confirm the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract  This paper presents the splitting cubes, a fast and robust technique for performing interactive virtual cutting on deformable objects. The technique relies on two ideas. The first one is to embed the deformable object in a regular grid, to apply the deformation function to the grid nodes and to interpolate the deformation inside each cell from its 8 nodes. The second idea is to produce a tessellation for the boundary of the object on the base of the intersections of such boundary with the edges of the grid. Please note that the boundary can be expressed in any way; for example it can be a triangle mesh, an implicit or a parametric surface. The only requirement is that the intersection between the boundary and the grid edges can be computed. This paper shows how the interpolation of the deformation inside the cells can be used to produce discontinuities in the deformation function, and the intersections of the cut surface can be used to visually show the cuts on the object. The splitting cubes is essentially a tessellation algorithm for growing, deformable surface, and it can be applied to any method for animating deformable objects. In this paper the case of the mesh-free methods (MMs) is considered: in this context, we described a practical GPU friendly method, that we named the extended visibility criterion, to introduce discontinuities of the deformation. [ABSTRACT FROM AUTHOR]

In this paper, the development of new hybrid group iterative methods for the numerical solution of a two-dimensional time-fractional cable equation is presented. We use Laplace transform method to approximate the time fractional derivative which reduces the problem into an approximating partial differential equation. The obtained partial differential equation is solved by four-point group iterative methods derived from two implicit finite difference schemes. Matrix norm analysis together with mathematical induction are utilized to investigate the stability and convergence properties. A comparative study with the recently developed hybrid standard point (HSP) iterative method accompanied by their computational cost analysis are also given. Numerical experiments are conducted to demonstrate the superiority of the proposed hybrid group iterative methods over the HSP iterative method in terms of the number of iterations, computational cost as well as the CPU times. [ABSTRACT FROM AUTHOR]

Global optimization problems are often approached by branch and bound algorithms which use linear relaxations of the nonlinear constraints computed from the current variable bounds. This paper studies how to derive safe linear relaxations to account for numerical errors arising when computing the linear coefficients. It first proposes two classes of safe linear estimators for univariate functions. Class-1 estimators generalize previously suggested estimators from quadratic to arbitrary functions, while class-2 estimators are novel. When they apply, class-2 estimators are shown to be tighter theoretically (in a certain sense) and almost always tighter numerically. The paper then generalizes these results to multivariate functions. It shows how to derive estimators for multivariate functions by combining univariate estimators derived for each variable independently. Moreover, the combination of tight class-1 safe univariate estimators is shown to be a tight class-1 safe multivariate estimator. Finally, multivariate class-2 estimators are shown to be theoretically tighter (in a certain sense) than multivariate class-1 estimators. [ABSTRACT FROM AUTHOR]

In this paper, we study the global existence and decay rates of the solutions near Maxwellian for non-linear Fokker-Planck equations in the whole space. The global existence is proved by combining uniform-in-time energy estimates with local solution constructed by Picard type iteration sequence. The decay rates of the nonlinear model is obtained by using the precise spectral analysis of the linearized Fokker-Planck operator as well as the energy method. The nonlinearity in the model brings new difficulty to the energy estimates, which is resolved by additional tailored weighted-in-v energy estimates suitable for Fokker-Planck operators. [ABSTRACT FROM AUTHOR]

The asymptotic properties of nonoscillating solutions of Emden-Fowler-type equations of arbitrary order are considered. The paper contains the results of the study of the asymptotic properties of solutions with integer-valued asymptotics as well as of solutions arising from the rapid decrease of the coefficient of the equation. To analyze the asymptotic behavior of solutions of the equations, methods of power geometry are used. [ABSTRACT FROM AUTHOR]

In this paper, by linking Fokker-Planck equations with stochastic coupled systems, a new method is provided to investigate the existence of a stationary distribution of stochastic coupled systems. Based on the graph theory and the Lyapunov method, an appropriate Lyapunov function associated with stationary Fokker-Planck equations is constructed. Moreover, a Lyapunov-type theorem and a coefficients-type criterion are obtained to guarantee the existence of a stationary distribution. Furthermore, theoretical results are applied to explore the existence of a stationary distribution of stochastic predator-prey models with dispersal and a sufficient criterion is presented correspondingly. Finally, a numerical example is given to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, numerical solution of the FitzHugh-Nagumo (FN) equation is presented based on the nonstandard finite-difference (NSFD) scheme. At first, two exact finite-difference schemes for FN equation are obtained. Moreover, two NSFD schemes are presented for this equation. The positivity, boundedness, and local truncation error of the schemes are discussed. The numerical results obtained by the NSFD schemes are compared with the exact solution and some available methods, to verify the accuracy and efficiency of the NSFD schemes. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the cross-coupled Camassa-Holm system. First, we prove local well-posedness for the cross-coupled Camassa-Holm equations in $$H^s ({\mathbb {R}})$$ with $$s > 3/2$$ . Then, a blow-up criterion is established. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved non-local boundary value problem method to solve a Cauchy problem for the Laplace equation. It is known that the Cauchy problem for the Laplace equation is severely ill-posed, i.e., the solution does not depend continuously on the given Cauchy data. Convergence estimates for the regularized solutions are obtained under a-priori bound assumptions for the exact solution. Some numerical results are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we prove the 2-dimensional Bernstein theorem for a class of fourth order equations including Abreu's equation. The main ingredients of the paper are the a priori estimates and the proof of the strict convexity. [ABSTRACT FROM AUTHOR]

It is a well-known consequence of the Baker-Pixley-Theorem that any clone containing a near-unanimity operation is finitely generated, leading to the question what arity the generating functions must have. In this paper, we show that, for arbitrary d ≥ 2 and large enough n, ( n − 1) − 1 is the smallest integer k such that, for every clone C on an n-element set that contains a ( d + 1)-ary near-unanimity operation, C generates C. [ABSTRACT FROM AUTHOR]

freeoid over a (normally, infinite) set of variables X is defined to be a pair ( W, E), where W is a superset of X, and E is a submonoid of W containing just one extension of every mapping X → W. For instance, if W is a relatively free algebra over a set of free generators X, then the pair F( W) := ( W, End( W)) is a freeoid. In the paper, the kernel equivalence and the range of the transformation F are characterized. Freeoids form a category; it is shown that the transformation F gives rise to a functor from the category of relatively free algebras to the category of freeoids which yields a concrete equivalence of the first category to a full subcategory of the second one. Also, the concept of a model of a freeoid is introduced; the variety generated by a free algebra W is shown to be concretely equivalent to the category of models of F( W). The sets X, W, and the algebras W may generally be many-sorted. [ABSTRACT FROM AUTHOR]

In this paper we describe a construction which produces classes in compactifications of the moduli space of curves. This construction extends a construction of Kontsevich which produces classes in the open moduli space from the initial data of a cyclic A∞-algebra. The initial data for our construction are what we call a ‘quantum A∞-algebra’, which arises as a type of deformation of a cyclic A∞-algebra. The deformation theory for these structures is described explicitly. We construct a family of examples of quantum A∞-algebras which extend a family of cyclic A∞-algebras, introduced by Kontsevich, which are known to produce all the kappa classes using his construction. [ABSTRACT FROM AUTHOR]

In this paper we study some optimization problems for nonlinear elastic membranes. More precisely, we consider the problem of optimizing the cost functional $\mathcal {J}(u)=\int_{\partial\Omega}f(x)u\,\mathrm {d}\mathcal {H}^{N-1}$ over some admissible class of loads f where u is the (unique) solution to the problem −Δ p u+| u| p−2 u=0 in Ω with | ∇ u| p−2 u ν= f on ∂Ω. [ABSTRACT FROM AUTHOR]

We found a minor error in the proof of paper “Universal Alignment Probability Revisited” by S.Y. Lin and Y.C. Ho (J. Optim. Theory Appl. 113(2):399–407, ). In this note, we give a counterexample and explain the reason. We also show that the conclusion of that paper is still correct despite this minor error. A new proof of the conclusion is given. [ABSTRACT FROM AUTHOR]

Abstract  A model second-order elliptic equation on a general convex polyhedral domain in three dimensions is considered. The aim of this paper is twofold: First sharp Hölder estimates for the corresponding Green’s function are obtained. As an applications of these estimates to finite element methods, we show the best approximation property of the error in $${W^1_{\infty}}$$ . In contrast to previously known results, $${W_p^{2}}$$ regularity for p > 3, which does not hold for general convex polyhedral domains, is not required. Furthermore, the new Green’s function estimates allow us to obtain localized error estimates at a point. [ABSTRACT FROM AUTHOR]

In this paper, we extend Guo and Xia’s necessary condition which has been presented by Guo and Xia (Fuzzy optimizat Decis Mak 5: 33–47, 2006) in order to study the finitely many constraints of fuzzy relation inequalities and optimize a linear objective function on this region which is defined by the fuzzy max–min operator. The new condition provides a means for removing the unnecessary paths resulting from Guo and Xia’s paths. Also, an algorithm and two numerical examples are offered to abbreviate and illustrate the steps of the resolution process of the problem. [ABSTRACT FROM AUTHOR]

In this paper, we present an efficient Newton-like method with fifth-order convergence for nonlinear equations. The algorithm is free from second derivative and it requires four evaluations of the given function and its first derivative at each iteration. As a consequence, its efficiency index is equal to 4 √5 which is better than that of Newton's method √2. Several examples demonstrate that the presented algorithm is more efficient and performs better than Newton's method. [ABSTRACT FROM AUTHOR]

Abstract  The seminal paper by Kasner (Am. J. Math. 43, 217–221, 1921) is reprinted here, together with an editorial comment on its lasting scientific relevance, and a biography of the author. [ABSTRACT FROM AUTHOR]

Abstract  In this paper, we derive one-parameter families of Newton, Halley, Chebyshev, Chebyshev-Halley type methods, super-Halley, C-methods, osculating circle and ellipse methods respectively for finding simple zeros of nonlinear equations, permitting f ′ (x) = 0 at some points in the vicinity of the required root. Halley, Chebyshev, super-Halley methods and, as an exceptional case, Newton method are seen as the special cases of the family. All the methods of the family and various others are cubically convergent to simple roots except Newton’s or a family of Newton’s method. [ABSTRACT FROM AUTHOR]

To solve nonlinear complementarity problems (NCP), the logarithmicquadratic proximal (LQP) method solves a system of nonlinear equations at each iteration. In this paper, the iterates generated by the original LQP method are extended by explicit formulas and thus an extended LQP method is presented. It is proved theoretically that the lower bound of the progress obtained by the extended LQP method is greater than that by the original LQP method. Preliminary numerical results are provided to verify the theoretical assertions and the effectiveness of both the original and the extended LQP method. [ABSTRACT FROM AUTHOR]

We consider quasihomogeneous strings with piecewise constant density and derive the quasihomogeneity condition. For a small number of string components, we present explicit formulas for reconstructing a string from its part. For an arbitrary number of string components, we construct a theory of matrices of special form (that we call distinguished) and present an algorithm for string reconstruction from its part. [ABSTRACT FROM AUTHOR]

This paper studies a class of transport equations arising from stochastic models in congestion control. This class contains two cases of loss models as particular cases: the rate-independent case where the packet loss rate is independent of the throughput of the flow and the rate-dependent case where it depends on it. This class of equations covers both the case of persistent and of non-persistent flows. For the first time, we give a direct proof of the fact that there is a unique density solving the associated differential equation. This density and its mean value are provided as closed form expressions. [ABSTRACT FROM AUTHOR]

We will show in this paper that if λ is very close to 1, then can be attained, where M is a compact–manifold with boundary. This result gives a counter–example to the conjecture of de Figueiredo and Ruf in their paper titled "On an inequality by Trudinger and Moser and related elliptic equations" ( Comm. Pure. Appl. Math., 55, 135–152, 2002). [ABSTRACT FROM AUTHOR]

The paper addresses matrix spaces, whose properties and dynamics are determined by Dirac matrices in Riemannian spaces of different dimension and signature. Among all Dirac matrix systems there are such ones, which nontrivial scalar, vector or other tensors cannot be made up from. These Dirac matrix systems are associated with the vacuum state of the matrix space. The simplest vacuum system realization can be ensured using the orthonormal basis in the internal matrix space. This vacuum system realization, however, is not unique. The case of 7-dimensional Riemannian space of signature 7(−) is considered in detail. In this case two basically different vacuum system realizations are possible: (1) with using the orthonormal basis; (2) with using the oblique-angled basis, whose base vectors coincide with the simple roots of the Lie algebra E8. [ABSTRACT FROM AUTHOR]

In this paper we provide estimates of the rates of convergence of monotone approximation schemes for non-convex equations in one space-dimension. The equations under consideration are the degenerate elliptic Isaacs equations with x-depending coefficients, and the results applies in particular to certain finite difference methods and control schemes based on the dynamic programming principle. Recently, Krylov, Barles, and Jakobsen obtained similar estimates for convex Hamilton–Jacobi–Bellman equations in arbitrary space-dimensions. Our results are only valid in one space-dimension, but they are the first results of this type for non-convex second-order equations. [ABSTRACT FROM AUTHOR]

Conventional schedulers schedule operations in dependence order and never revisit or undo a scheduling decision on any operation. In contrast, backtracking schedulers may unschedule operations and can often generate better schedules. This paper develops and evaluates the backtracking approach to fill branch delay slots. We first present the structure of a generic backtracking scheduling algorithm and prove that it terminates. We then describe two more aggressive backtracking schedulers and evaluate their effectiveness. We conclude that aggressive backtracking-based instruction schedulers can effectively improve schedule quality by eliminating branch delay slots with a small amount of additional computation. [ABSTRACT FROM AUTHOR]

This paper focuses on the global regularity problem for a family of active scalar equations with fractional dissipation. We obtain an explicit lower bound on the local existence of solutions, the eventual regularity of solutions and the global regularity of solutions for large initial data for the supercritical active scalar equations. In addition, a new regularity criterion is presented for the supercritical case which is used to study the eventual regularity. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonoscillation of the higher-order nonlinear delay dynamic equation where $\mathbb{T}$ is a scale with $\sup\mathbb{T}=\infty$, $t_{0}\in\mathbb{T}$, and $[t_{0},\infty)_{\mathbb{T}}= \{t\in\mathbb{T}:t\geq t_{0}\}$. We obtain some sufficient conditions for all solutions of this equation to be nonoscillatory. [ABSTRACT FROM AUTHOR]

We initiate the study of an evolution problem associated to a mean field type equation. In the present paper, we give a compactness result for solutions of a perturbed mean field type equation. Our method is based on blow-up analysis relying on integral estimates. This result will be used in Casteras () to prove the convergence of a flow associated to a mean field type equation. [ABSTRACT FROM AUTHOR]

The bondage number b( G) of a graph G is the cardinality of a minimum set of edges whose removal from G results in a graph with a domination number greater than that of G. In this paper, we obtain the exact value of the bondage number of the strong product of two paths. That is, for any two positive integers m ⩾ 2 and n ⩾ 2, b( P ⊠ P) = 7 − r( m) − r( n) if ( r( m), r( n)) = (1, 1) or (3, 3), 6 − r( m) − r( n) otherwise, where r( t) is a function of positive integer t, defined as r( t) = 1 if t ≡ 1 (mod 3), r( t) = 2 if t ≡ 2 (mod 3), and r( t) = 3 if t ≡ 0 (mod 3). [ABSTRACT FROM AUTHOR]

In this paper, we establish a new regularity criterion for the 3D incompressible MHD equations involving partial components of the velocity gradient and magnetic fields. [ABSTRACT FROM AUTHOR]

Let p be a prime and let A = ( a,..., a) be a sequence of nonzero elements in $\mathbb{F}_p $. In this paper, we study the set of all 0-1 solutions to the equation $$a_1 x_1 + \cdots + a_\ell x_\ell = 0$$ We prove that whenever ℓ≥ p, this set actually characterizes A up to a nonzero multiplicative constant, which is no longer true for ℓ< p. The critical case ℓ= p is of particular interest. In this context, we prove that whenever ℓ= p and A is nonconstant, the above equation has at least p−1 minimal 0-1 solutions, thus refining a theorem of Olson. The subcritical case ℓ= p−1 is studied in detail also. Our approach is algebraic in nature and relies on the Combinatorial Nullstellensatz as well as on a Vosper type theorem. [ABSTRACT FROM AUTHOR]

For effectively solving dynamic matrix equation (DME) problems, a non-convex and bound-constrained zeroing neural network (NCBC-ZNN) model is designed to relax the convex constraint on the demand of activation function and achieve robustness against various noises. Moreover, rigorous mathematical analyses and proofs are presented under the circumstances of noise-free and noise-perturbed to theoretically investigate the global convergence and robustness of the proposed NCBC-ZNN model. In addition, simulative experiments are further provided to substantiate the superior performance of the proposed model in solving the DME problem compared with the existing state-of-the-art models. Finally, the proposed model combines the constrained energy minimization (CEM) algorithm to solve the hyperspectral image multi-target detection (HIMTD) problem. Compared with existing schemes, our method is competitive in terms of accuracy. [ABSTRACT FROM AUTHOR]

The paper deals with solutions to Emden-Fowler-type equations of any arbitrary order. The asymptotic properties of solutions to these equations are studied, and a systematic survey of numerous uncoordinated results of analysis of continuable and noncontinuable solutions is given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce mixed generalized quasi-equilibrium problems and show some sufficient conditions on the existence of their solutions. As special cases, we obtain several results for different mixed quasi-equilibrium problems, mixed quasi-variational inclusions problems and mixed quasi-relation problems etc. [ABSTRACT FROM AUTHOR]