In this study, we prove an existence result of renormalized solutions for nonlinear parabolic equations of the type $$ displaystylefrac{partial b(x,u)}{partial t} -mbox{div}>a(x,t,u,nabla u)-mbox{div}> Phi(x,t,u)= f quadmbox{in }{Q_T=Omegatimes (0,T)}, $$ where $b(x,cdot)$ is a strictly increasing $C^1$-function for every $xinOmega$ with $b(x,0)=0$, the lower order term $Phi$ satisfies a natural growth condition described by the appropriate Orlicz function $M$ and $f$ is an element of $L^1(Q_T)$. We don't assume any restriction neither on $M$ nor on its conjugate $overline{M}$.
We introduce the concept of Isbell convexity in fuzzy quasi-metric spaces, which we call fuzzy Isbell convexity. This idea extends Isbell convexity (or q-hyperconvexity) in quasi-metric spaces to fuzzy quasi metric spaces. We show that fuzzy Isbell convexity is preserved by certain $F$-bounded subsets and the space of non-negative function pairs of the fuzzy quasi-metric space.
In this paper, for admissible and integrable function $psi$ in $L^2(mathbb{R}^n)$, the multi-dimensional continuous wavelet transform on Sobolev spaces is defined. The inversion formula for this transform on Sobolev spaces is established and as a result it is concluded that there is an isometry of Sobolev spaces $H_s(mathbb{R}^n)$ into $H_{0,s}(mathbb{R}^n times mathbb{R}^+_0times S^{n-1})$, for arbitrary real $s$. Also, among other things, it is shown that the range of this transform is a reproducing kernel Hilbert space and the reproducing kernel is found.
Let $(X,d)$ and $(Y,rho)$ be compact metric spaces, $tau$ and $eta$ be Lipschitz involutions on $ X$ and $Y$, respectively, $mathcal{A}=Lip(X,d,tau)$ and $mathcal{B}=Lip(Y,rho,eta)$, where $Lip(X,d,tau)=lbrace fin Lip(X,d):fcirctau=bar{f}rbrace $. For each $fin mathcal{A}$, $sigma_{pi,mathcal{A}}(f)$ denotes the peripheral spectrum of $f$. We prove that if $S_{1},S_{2}:mathcal{A}rightarrow mathcal{A}$ and $T_{1},T_{2}:mathcal{A}rightarrow mathcal{B}$ are surjective mappings that satisfy $sigma_{pi,mathcal{B}}(T_{1}(f)T_{2}(g))=sigma_{pi,mathcal{A}}(S_{1}(f)S_{2}(g))$ for all $f,gin mathcal{A}$, then there are $kappa_{1},kappa_{2}in Lip(Y,rho,eta)$ with $kappa_{1}kappa_{2}=1_{Y}$ and a Lipschitz homeomorphism $varphi$ from $(Y,rho)$ to $(X,d)$ with $tau circvarphi=varphi circ eta$ on $Y$ such that $T_{j}(f)=kappa_{j}cdot(S_{j}(f)circvarphi)$ for all $fin mathcal{A}$ and $j=1,2$. Moreover, we show that the same result holds for surjective mappings $S_{1},S_{2}:mathcal{A}rightarrow mathcal{A}$ and $T_{1},T_{2}:mathcal{A}rightarrow mathcal{B}$ that satisfy $sigma_{pi,mathcal{B}}(T_{1}(f)T_{2}(g))capsigma_{pi,mathcal{A}}(S_{1}(f)S_{2}(g))neqemptyset$ for all $f,gin mathcal{A}$.
In this paper, we consider a multi-species Lotka-Volterra type competitive system with delays and feedback controls on time scales. A general criteria on the permanence is established and then by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence anduniform asymptotic stability of unique positive almost periodic solution of the system.
Let $psiin L^{infty}(mathbb{U_{+}}),$ where $mathbb{U_{+}}$ is the upper half plane in $mathbb{C}$ and $S_{psi}$ be the little Hankel operator with symbol $psi$ defined on the Bergman space $L_{a}^{2}(mathbb{U}_{+}).$ In this paper we have shown that if $S_{psi}$ is of finite rank then $psi=varphi+chi,$ where $chiin left(overline{L_{a}^{2}(mathbb{U}_{+})}right)^{perp}bigcap L^{infty}(mathbb{U}_{+})$ and $overline{varphi}$ is a linear combination of $d_{overline{w}}, win mathbb{U}_{+}$ and some of their derivatives.
This article presents an account of the fundamentals of the discrete group approach for analysis and integration of practical differential equations. In this paper, by means of appropriate transformations, the nonlinear Burgers equation is transformed into the other class of the second-order differential equation of the Emden-Fowler type and this Emden-Fowler equation reduces to the nonlinear Abel equations. This approach shows that, under this transformations of discrete group, the solution of reference equation can be transformed into the solution of the transformed equation. Under such a conditions, we approach to the determine some solutions for the Abel, Burgers, Emden-Fowler and heat equations.
We study the existence of solutions for quasilinear parabolic systems of the form [partial_tu-text{div},sigma(x,t,Du)=fquadtext{in};Q=Omegatimes(0,T),] whose right hand side belongs to $W^{-1,x}L_{overline{M}}(Q;R^m)$, supplemented with the conditions $u=0$ on $partialOmegatimes(0,T)$ and $u(x,0)=u_0(x)$ in $Omega$. By using a mild monotonicity condition for $sigma$, namely strict quasimonotone, and the theory of Young measures, we deduce the needed result.
In this work, a Gruss inequality for positive Hilbert space operators is proved. So, some numerical radius inequalities are proved. On the other hand, based on a non-commutative Binomial formula, a non-commutative upper bound for the numerical radius of the summand of two bounded linear Hilbert space operators is proved. A commutative version is also obtained as well.
Let K be a field and E be a directed graph, called quiver in the following, and let A = KE be the path algebra that corresponds to E with coefficients in K. An A-module M is a c-prime module in the sense that rm = 0 for one m in M and r in A implies that either r annihilates all M or m = 0. In this paper, we prove that for any acyclic graph E, an A-module M is c-prime if and only if it is simple. The primeness of simple modules over Leavitt path algebras is also discussed. We prove that some classes of simple modules over Leavitt path algebras, are not c-prime modules.
We introduce the concept of almost thick chaos and continuously almost thick transitivity for continuous maps and nonautonomous dynamical systems (NDS). We show that NDS $f_{1,infty}$ is sensitive if it is thick transitive and syndetic. Under certain conditions, we show that NDS $(X,f_{1,infty})$ generated by a sequence $(f_n)$ of continuous maps on $X$ converging uniformly to $f$ is almost thick transitive if and only if $(X,f)$ is almost thick transitive. Moreover, we prove that if $f_{1,infty}$ is continuously almost thick transitive and syndetic, then it is strongly topologically ergodic. In addition, the relationship between the large deviations theorem and almost thick chaos is studied.
In the last decade, the notions of function-f-ϵ-chainability, uniformly function-f-ϵ-chainability, function-f-ϵ-chainable sets and locally functionf-chainable sets were studied in some papers. We show that the notions of function-f-ϵ-chainability and uniformly function-f-ϵ-chainability are equivalent to the notion of non-ultrapseudocompactness in topological spaces. Also, all of these are equivalent to the condition that each pair of non-empty subsets (resp., subsets with non-empty interiors) is function-f-ϵ-chainable (resp., locally function-f-chainable). Further, we provide a criterion for connectedness with covers. In the paper Characterization of ϵ-chainable sets in metric spaces (Indian J. Pure Appl. Math. 33 (2002), no. 6, 933{940), the chainability of a pair of subsets in a metric space has been defined wrongly and consequently Theorem 1 and Theorem 5 are found to be wrong. We rectify their definition appropriately and consequently, we give appropriate results and counterexamples.
In this paper, we introduce an iterative algorithm based on the well-known Krasnoselskii-Mann's method for finding a common element of the set of fixed points of multivalued demicontractive mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Then, strong convergence of the scheme to a common element of the two sets is proved without imposing any compactness condition on the mapping or the space. We further applied our results to solve some optimization problems. Our results improve many recent results using Krasnoselskii-Mann's algorithm for solving nonlinear problems.
In this paper, we further investigated the $SS mathcal{I} H$ and $S mathcal{I} H$ properties introduced by Das et. al recently. It is shown that regular-closed $G_delta$ subspace of $SS mathcal{I} H$ (resp., $S mathcal{I} H$) is not $SS mathcal{I} H$ (resp., $S mathcal{I} H$). The preservation properties of these spaces are studied under some maps. Also $SS mathcal{I} H$ and $S mathcal{I} H$ properties are investigated in Alexandroff space.
A category C is called cartesian closed provided that it has finite products and for each C-object A the functor (A×−) : A → A has a right adjoint. It is well known that the category TML of topological molecular lattices with generalized order homomorphims in the sense of Wang is both complete and cocomplete, but it is not cartesian closed. In this paper, we introduce a cartesian closed subcategory of this category.
A finite group G is called (l,m, n)-generated}, if it is a quotient group of the triangle group T(l,m, n) = . In [23], Moori posed the question of finding all the (p,q,r) triples, where p, q and r are prime numbers, such that a non-abelian finite simple group G is a (p,q,r)-generated. In this paper we establish all the (p,q,r)-generations of the alternating group A_11.$ GAP [14] and the Atlas of finite group representations[28] are used in our computations.
This article presents a solution for a class of singularly perturbed convection with delay problems arising in control theory. The approach of extending Taylor's series for the convection term gives to a bad approximation when the delay is not smaller order of singular perturbation parameter. To handle the delay term, we model an interesting mesh form such that the delay term lies on mesh points. The parametric cubic spline is adapted to the continuous problem on a specially designed mesh. The truncation error for the proposed method is derived. Numerical examples are experimented to examine the effect of the delay parameter on the layer structure.
The goal of this note is to investigate some properties of the critical point equations on the $3-$dimensional $f-$ cosymplectic manifolds. We obtain some geometric equations on the $3-$dimensional $f-$ cosymplectic manifolds which admit critical point equations. We give a relation between $f$ and $tilde{f}$ for a CPE metric on the three dimensional $f-$cosymplectic manifold to be Einstein. Also we obtain an eigenvalue of the Laplace operator on the $3-$dimensional $f-$ cosymplectic manifolds with CPE metrics.
In this article, we introduce some metallic structures on the tangent bundle of a P-Sasakian manifold by complete lift, horizontal lift and vertical lift of a P-Sasakian structure $(ϕ, η,ξ)$ on tangent bundle. Then we investigate the integrability and parallelity of these metallic structures.
In this article, we have introduced the concept of geodesic (α,E)-invex set and by using this concept the notion of geodesic (α,E)-preinvex functions and geodesic (α,E)-invex functions are developed on a Riemannian manifold. Moreover, several properties and results are deduced within aforesaid functions. An example is also constructed to illustrate the definition of geodesic (α,E)-invex set. We have also established an important relation between geodesic (α,E)-preinvex function and geodesic (α,E)-invex function in a complete Riemannian manifold.
