Sahand Communications in Mathematical AnalysisSahand Communications in Mathematical Analysis
http://scma.maragheh.ac.ir/
Fri, 17 Aug 2018 17:32:32 +0100FeedCreatorSahand Communications in Mathematical Analysis
http://scma.maragheh.ac.ir/
Feed provided by Sahand Communications in Mathematical Analysis. Click to visit.On generalized topological molecular lattices
http://scma.maragheh.ac.ir/article_27148_4979.html
In this paper, we introduce the concept of the generalized topological molecular lattices as a generalization of Wang's topological molecular lattices, topological spaces, fuzzy topological spaces, L-fuzzy topological spaces and soft topological spaces. Topological molecular lattices were defined by closed elements, but in this new structure we present the concept of the open elements and define a closed element by the pseudocomplement of an open element. We have two structures on a completely distributive complete lattice, topology and generalized co-topology which are not dual to each other. We study the basic concepts, in particular separation axioms and some relations among them.Sat, 31 Mar 2018 19:30:00 +0100Similar generalized frames
http://scma.maragheh.ac.ir/article_24628_4979.html
Generalized frames are an extension of frames in Hilbert spaces and Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an orthogonal projection. Moreover, a $g$-frame is obtained by two the $g$-frames and its operator duals are investigated. Finally, the dilation of $g$-frames is studied.Sat, 31 Mar 2018 19:30:00 +0100On $L^*$-proximate order of meromorphic function
http://scma.maragheh.ac.ir/article_23127_4979.html
In this paper we introduce the notion of $L^{* }$-proximate order of meromorphic function and prove its existence.Sat, 31 Mar 2018 19:30:00 +0100The spectral properties of differential operators with matrix coefficients on elliptic systems ...
http://scma.maragheh.ac.ir/article_27152_4979.html
Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estimate the resolvent of the operator $L$ on the one-dimensional space $ L_{2}(Omega)$ using some analytic methods.Sat, 31 Mar 2018 19:30:00 +0100Existence of three solutions for a class of quasilinear elliptic systems involving the ...
http://scma.maragheh.ac.ir/article_27915_4979.html
The aim of this paper is to obtain three weak solutions for the Dirichlet quasilinear elliptic systems on a bonded domain. Our technical approach is based on the general three critical points theorem obtained by Ricceri.Sat, 31 Mar 2018 19:30:00 +0100Products Of EP Operators On Hilbert C*-Modules
http://scma.maragheh.ac.ir/article_28402_4979.html
In this paper, the special attention is given to the product of two modular operators, and when at least one of them is EP, some interesting results is made, so the equivalent conditions are presented that imply the product of operators is EP. Also, some conditions are provided, for which the reverse order law is hold. Furthermore, it is proved that $P(RPQ)$ is idempotent, if $RPQ$† has closed range, for orthogonal projections $P,Q$ and $R$.Sat, 31 Mar 2018 19:30:00 +0100$C^{*}$-semi-inner product spaces
http://scma.maragheh.ac.ir/article_28403_4979.html
In this paper, we introduce a generalization of Hilbert $C^*$-modules which are pre-Finsler modules, namely, $C^{*}$-semi-inner product spaces. Some properties and results of such spaces are investigated, specially the orthogonality in these spaces will be considered. We then study bounded linear operators on $C^{*}$-semi-inner product spaces.Sat, 31 Mar 2018 19:30:00 +0100Some fixed point theorems for $C$-class functions in $b$-metric spaces
http://scma.maragheh.ac.ir/article_28505_4979.html
In this paper, via $C$-class functions, as a new class of functions, a fixed theorem in complete $b$-metric spaces is presented. Moreover, we study some results, which are direct consequences of the main results. In addition, as an application, the existence of a solution of an integral equation is given.Sat, 31 Mar 2018 19:30:00 +0100Convergence of Integro Quartic and Sextic B-Spline interpolation
http://scma.maragheh.ac.ir/article_27153_4979.html
In this paper, quadratic and sextic B-splines are used to construct an approximating function based on the integral values instead of the function values at the knots. This process due to the type of used B-splines (fourth order or sixth order), called integro quadratic or sextic spline interpolation. After introducing the integro quartic and sextic B-spline interpolation, their convergence is discussed. The interpolation errors are studied. Numerical results illustrate the efficiency and effectiveness of the new interpolation method.Sat, 31 Mar 2018 19:30:00 +0100Somewhat pairwise fuzzy $\alpha$-irresolute continuous mappings
http://scma.maragheh.ac.ir/article_28222_4979.html
The concept of somewhat pairwise fuzzy $alpha$-irresolute continuous mappings and somewhat pairwise fuzzy irresolute $alpha$-open mappings have been introduced and studied. Besides, some interesting properties of those mappings are given.Sat, 31 Mar 2018 19:30:00 +0100$L$-Topological Spaces
http://scma.maragheh.ac.ir/article_28387_4979.html
‎By substituting the usual notion of open sets in a topological space $X$ with a suitable collection of maps from $X$ to a frame $L$, we introduce the notion of L-topological spaces. Then, we proceed to study the classical notions and properties of usual topological spaces to the newly defined mathematical notion. Our emphasis would be concentrated on the well understood classical connectedness, quotient and compactness notions, where we prove the Thychonoff's theorem and connectedness property for ultra product of $L$-compact and $L$-connected topological spaces, respectively.Sat, 31 Mar 2018 19:30:00 +0100Fuzzy $e$-regular spaces and strongly $e$-irresolute mappings
http://scma.maragheh.ac.ir/article_28031_4979.html
The aim of this paper is to introduce fuzzy ($e$, almost) $e^{*}$-regular spaces in $check{S}$ostak's fuzzy topological spaces. Using the $r$-fuzzy $e$-closed sets, we define $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points and their properties. Moreover, we investigate the relations among $r$-($r$-$theta$-, $r$-$etheta$-) $e$-cluster points, $r$-fuzzy ($e$, almost) $e^{*}$-regular spaces and their functions.Sat, 31 Mar 2018 19:30:00 +0100On some results in the light of generalized relative Ritt order of entire functions represented ...
http://scma.maragheh.ac.ir/article_23647_0.html
In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.Wed, 11 Jan 2017 20:30:00 +0100Linear Maps preserving invertibility or spectral radius on some $C^{*}$-algebras
http://scma.maragheh.ac.ir/article_23702_0.html
Let $A$ be a unital $C^{*}$-algebra which has a faithful state. If $varphi:Arightarrow A$ is a unital linear map which is bijective and invertibility preserving or surjective and spectral radius preserving, then $varphi$ is a Jordan isomorphism. Also, we discuss other types of linear preserver maps on $A$.Sun, 15 Jan 2017 20:30:00 +0100Extensions of Saeidi's Propositions for finding a unique solution of a variational inequality ...
http://scma.maragheh.ac.ir/article_25887_0.html
Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B : C rightarrow E $ be a nonlinear map, and let $u, v$ be positive numbers. In this paper, we show that the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for finding a unique solution of the variational inequality for $(u, v)$-cocoercive mappings in Banach spaces.Sat, 17 Jun 2017 19:30:00 +0100Some properties of reproducing Kernel Banach and Hilbert spaces
http://scma.maragheh.ac.ir/article_27822_0.html
This paper is devoted to the study of reproducing kernel Hilbert spaces. We focus on multipliers of reproducing kernel Banach and Hilbert spaces. In particular, we try to extend this concept and prove some related theorems. Moreover, we focus on reproducing kernels in vector-valued reproducing kernel Hilbert spaces. In particular, we extend reproducing kernels to relative reproducing kernels and prove some theorems in this subject.Tue, 10 Oct 2017 20:30:00 +0100On the integral representations of generalized relative type and generalized relative weak type ...
http://scma.maragheh.ac.ir/article_27953_0.html
In this paper we wish to establish the integral representations of generalized relative type and generalized relative weak type as introduced by Datta et al [9]. We also investigate their equivalence relation under some certain conditions.Sun, 15 Oct 2017 20:30:00 +0100On character space of the algebra of BSE-functions
http://scma.maragheh.ac.ir/article_27982_0.html
Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterization of $Delta(C_{rm{BSE}}(Delta(A)))$ and in the general case we give a partial answer. Also, using the Fourier algebra, we show that $C_{rm{BSE}}(Delta(A))$ is not a $C^*$-algebra in general. Finally for some subsets $E$ of $A^*$, we define the subspace of BSE-like functions on $Delta(A)cup E$ and give a nice application of this space related to Goldstine's theorem.Tue, 17 Oct 2017 20:30:00 +0100On Fuzzy $e$-open Sets, Fuzzy $e$-continuity and Fuzzy $e$-compactness in Intuitionistic Fuzzy ...
http://scma.maragheh.ac.ir/article_28223_0.html
The purpose of this paper is to introduce and study the concepts of fuzzy $e$-open set, fuzzy $e$-continuity and fuzzy $e$-compactness in intuitionistic fuzzy topological spaces. After giving the fundamental concepts of intuitionistic fuzzy sets and intuitionistic fuzzy topological spaces, we present intuitionistic fuzzy $e$-open sets and intuitionistic fuzzy $e$-continuity and other results related topological concepts. Several preservation properties and some characterizations concerning intuitionistic fuzzy $e$-compactness have been obtained.Tue, 31 Oct 2017 20:30:00 +0100On generators in Archimedean copulas
http://scma.maragheh.ac.ir/article_28401_0.html
This study after reviewing construction methods of generators in Archimedean copulas (AC), proposes several useful lemmas related with generators of AC. Then a new trigonometric Archimedean family will be shown which is based on cotangent function. The generated new family is able to model the low dependence structures.Sat, 11 Nov 2017 20:30:00 +0100A class of new results in FLM algebras
http://scma.maragheh.ac.ir/article_28459_0.html
In this paper, we first derive some results by using the Gelfand spectrum and spectrum in FLM algebras. Then, the characterizations of multiplicative linear mappings are also discussed in these algebras.Tue, 14 Nov 2017 20:30:00 +0100A coupled random fixed point result with application in polish spaces
http://scma.maragheh.ac.ir/article_28506_0.html
In this paper, we present a new concept of random contraction and prove a coupled random fixed point theorem under this condition which generalizes stochastic Banach contraction principle. Finally, we apply our contraction to obtain a solution of random nonlinear integral equations and we present a numerical example.Sun, 19 Nov 2017 20:30:00 +0100On the Taylor sequence spaces of non-absolute type which include the spaces $\ell_p \ (1\leq p
http://scma.maragheh.ac.ir/article_28734_0.html
Let $T(r)$ denotes the Taylor method of order $r$ such that $rin mathbb{C}/ {0}$. Kiric{s}ci cite{k2} defined the Taylor sequence spaces of non-absolute type $t_0^r$ and $t_c^r$ and studied some of their proporties. In this paper, we introduce Taylor sequence spaces $t_p^r (1leq p<infty)$ and $t_infty^r$ consisting of all sequences whose $T(r)-$ transforms are in the spaces $ell_p$ and $ell_infty$, respectively. We investigate some properties and compute alpha-, beta- and gamma-duals of these spaces. Afterwards, we characterize some matrix classes of Taylor sequence spaces $t_p^r (1leq p<infty)$ and $t_infty^r$.Fri, 01 Dec 2017 20:30:00 +0100Some fixed point results on intuitionistic fuzzy metric spaces with a graph
http://scma.maragheh.ac.ir/article_29018_0.html
In 2006, Espinola and Kirk made a useful contribution on combining fixed point theory and graph theory. Recently, Reich and Zaslavski studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In this paper, by using the main idea of their work and the idea of combining fixed point theory on intuitionistic fuzzy metric spaces and graph theory, we present some iterative scheme results for $G$-fuzzy contractive and $G$-fuzzy nonexpansive mappings on graphs.Tue, 19 Dec 2017 20:30:00 +0100Rational Geraghty contractive mappings and fixed point theorems in ordered $b_2$-metric spaces
http://scma.maragheh.ac.ir/article_29263_0.html
In 2014, Zead Mustafa introduced $b_2$-metric spaces, as a generalization of both $2$-metric and $b$-metric spaces. Then new fixed point results for the classes of rational Geraghty contractive mappings of type I,II and III in the setup of $b_2$-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered $b_2$-metric spaces. These include Geraghty-type conditions, conditions that use comparison functions and almost generalized weakly contractive conditions. Berinde in [17-20] initiated the concept of almost contractions and obtained many interesting fixed point theorems. Results with similar conditions were obtained, textit{e.g.}, in [21] and [22]. In the last section of the paper, we define the notion of almost generalized $(psi ,varphi )_{s,a}$-contractive mappings and prove some new results. In particular, we extend Theorems 2.1, 2.2 and 2.3 of Ciric et.al. in [23] to the setting of $b_{2}$-metric spaces. Also, some examples are provided to illustrate the results presented herein and several interesting consequences of our theorems are also provided. The findings of the paper are based on generalization and modification of some recently reported theorems in the literature.Fri, 29 Dec 2017 20:30:00 +0100Observational modeling of the Kolmogorov-Sinai entropy
http://scma.maragheh.ac.ir/article_29983_0.html
In this paper, Kolmogorov-Sinai entropy is studied using mathematical modeling of an observer $ Theta $. The relative entropy of a sub-$ sigma_Theta $-algebra having finite atoms is defined and then the ergodic properties of relative semi-dynamical systems are investigated. Also, a relative version of Kolmogorov-Sinai theorem is given. Finally, it is proved that the relative entropy of a relative $ Theta $-measure preserving transformations with respect to a relative sub-$sigma_Theta$-algebra having finite atoms is affine.Fri, 02 Feb 2018 20:30:00 +0100Common fixed point theory in modified intuitionistic probabilistic metric spaces with common ...
http://scma.maragheh.ac.ir/article_30018_0.html
‎In this paper, we define the concepts of modified mbox{intuitionistic} probabilistic metric spaces, the property (E.A.) and the common property (E.A.) in modified intuitionistic probabilistic metric spaces.Then, by the common property (E.A.), we prove some common fixed point theorems in modified intuitionistic Menger probabilistic metric spaces satisfying an implicit relation.Mon, 05 Feb 2018 20:30:00 +0100On some properties of the max algebra system over tensors
http://scma.maragheh.ac.ir/article_30023_0.html
Recently we generalized the max algebra system to the class of nonnegative tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and investigate its properties relevant to the spectral theory.Mon, 05 Feb 2018 20:30:00 +0100Surjective real-Linear uniform isometries between complex function algebras
http://scma.maragheh.ac.ir/article_30145_0.html
In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A longrightarrow B$, where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${rm ER}left (A, Xright ) = {rm Ch}left (A, Xright )$ and ${rm ER}left (B, Yright ) = {rm Ch}left (B, Yright )$. Next, we give a description of $ T $ whenever $ A $ and $ B $ are complex function algebras and $ T $ does not assume to be unit-preserving.Fri, 23 Feb 2018 20:30:00 +0100The solvability of concave-convex quasilinear elliptic systems involving $p$-Laplacian and ...
http://scma.maragheh.ac.ir/article_30802_0.html
In this work, we study the existence of non-trivial multiple solutions for a class ofquasili near elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.Tue, 10 Apr 2018 19:30:00 +0100Inequality problems of equilibrium problems with application
http://scma.maragheh.ac.ir/article_30860_0.html
This paper aims at establishing the existence of results for a nonstandard equilibrium problems $(EP_{N})$. The solutions of this inequality are discussed in a subset $K$ (either bounded or unbounded) of a Banach spaces $X$. Moreover, we enhance the main results by application of some differential inclusion.Mon, 23 Apr 2018 19:30:00 +0100On approximate Birkhoff-James orthogonality and approximate $\ast$-orthogonality in ...
http://scma.maragheh.ac.ir/article_30861_0.html
We offer a new definition of $varepsilon$-orthogonality in normed spaces, and we try to explain some properties of which. Also we introduce some types of $varepsilon$-orthogonality in an arbitrary $C^ast$-algebra $mathcal{A}$, as a Hilbert $C^ast$-module over itself, and investigate some of its properties in such spaces. We state some results relating range-kernel orthogonality in $C^*$-algebras.Mon, 23 Apr 2018 19:30:00 +0100A certain class of character module homomorphisms on normed algebras
http://scma.maragheh.ac.ir/article_31199_0.html
For two normed algebras $A$ and $B$ with the character space $bigtriangleup(B)neq emptyset$ and a left $B-$module $X,$ a certain class of bounded linear maps from $A$ into $X$ is introduced. We set $CMH_B(A, X)$ as the set of all non-zero $B-$character module homomorphisms from $A$ into $X$. In the case where $bigtriangleup(B)=lbrace varphirbrace$ then $CMH_B(A, X)bigcup lbrace 0rbrace$ is a closed subspace of $L(A, X)$ of all bounded linear operators from $A$ into $X$. We define an equivalence relation on $CMH_B(A, X)$ and use it to show that $CMH_B(A, X)bigcuplbrace 0rbrace $ is a union of closed subspaces of $L(A, X)$. Also some basic results and some hereditary properties are presented. Finally some relations between $varphi-$amenable Banach algebras and character module homomorphisms are examined.Sun, 27 May 2018 19:30:00 +0100The norm estimates of pre-Schwarzian derivatives of spirallike functions and uniformly convex ...
http://scma.maragheh.ac.ir/article_31361_0.html
For a constant $alphain left(-frac{pi}{2},frac{pi}{2}right)$, we define a subclass of the spirallike functions, $SP_{p}(alpha)$, the set of all functions $fin mathcal{A}$[Releft{e^{-ialpha}frac{zf'(z)}{f(z)}right}geqleft|frac{zf'(z)}{f(z)}-1right|.]In the present paper, we shall give the estimate of the norm of the pre-Schwarzian derivative $mathrm{T}_f=f''/f'$ where $|mathrm{T}_f|=sup_{zin Delta} (1-|z|^2)|mathrm{T}_f(z)|$ for the functions in $SP_{p}(alpha)$.Sat, 09 Jun 2018 19:30:00 +0100Some fixed point results for the generalized $F$-suzuki type contractions in $b$-metric spaces
http://scma.maragheh.ac.ir/article_31379_0.html
Compared with the previous work, the aim of this paper is to introduce the more general concept of the generalized $F$-Suzuki type contraction mappings in $b$-metric spaces, and to establish some fixed point theorems in the setting of $b$-metric spaces. Our main results unify, complement and generalize the previous works in the existing literature.Mon, 11 Jun 2018 19:30:00 +0100$L^p$-Conjecture on hypergroups
http://scma.maragheh.ac.ir/article_31386_0.html
In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions for a weighted Lebesgue space $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$. Among the other things, we also show that if $K$ is a locally compact hypergroup and $p$ is greater than 2, $K$ is compact if and only if $m(K)$ is finite and $fast g$ exists for all $f,gin L^p(K)$, where $m$ is a left Haar measure for $K$, and in particular, if $K$ is discrete, $K$ is finite if and only if the convolution of any two elements of $L^p(K)$ exists.Mon, 11 Jun 2018 19:30:00 +0100Meir-Keeler type contraction mappings in $c_0$-triangular fuzzy metric spaces
http://scma.maragheh.ac.ir/article_31436_0.html
Proving fixed point theorem in a fuzzy metric space is not possible for Meir-Keeler contractive mapping. For this, we introduce the notion of $c_0$-triangular fuzzy metric space. This new space allows us to prove some fixed point theorems for Meir-Keeler contractive mapping. As some pattern we introduce the class of $alphaDelta$-Meir-Keeler contractive and we establish some results of fixed point for such a mapping in the setting of $c_0$-triangular fuzzy metric space. An example is furnished to demonstrate the validity of these obtained results.Sat, 16 Jun 2018 19:30:00 +0100The Integrating Factor Method in Banach Spaces
http://scma.maragheh.ac.ir/article_31559_0.html
The so called integrating factor method, used to find solutions of ordinary differential equations of a certain type, is well known. In this article, we extend it to equations with values in a Banach space. Besides being of interest in itself, this extension will give us the opportunity to touch on a few topics that are not usually found in the relevant literature. Our presentation includes various illustrations of our results.Sat, 23 Jun 2018 19:30:00 +0100On regular generalized $\delta$-closed sets in topological spaces
http://scma.maragheh.ac.ir/article_31670_0.html
In this paper a new class of sets called regular generalized $delta$-closed set (briefly rg$delta$-closed set)is introduced and its properties are studied. Several examples are provided to illustrate the behaviour of these new class of sets.Sat, 30 Jun 2018 19:30:00 +0100Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of ...
http://scma.maragheh.ac.ir/article_31813_0.html
In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].Tue, 10 Jul 2018 19:30:00 +0100Richardson and Chebyshev Iterative Methods by Using G-frames
http://scma.maragheh.ac.ir/article_31814_0.html
In this paper, we design some iterative schemes for solving operator equation $ Lu=f $, where $ L:Hrightarrow H $ is a bounded, invertible and self-adjoint operator on a separable Hilbert space $ H $. In this concern, Richardson and Chebyshev iterative methods are two outstanding as well as long-standing ones. They can be implemented in different ways via different concepts.In this paper, these schemes exploit the almost recently developed notion of g-frames which result in modified convergence rates compared with early computed ones in corresponding classical formulations. In fact, these convergence rates are formed by the lower and upper bounds of the given g-frame. Therefore, we can determine any convergence rate by considering an appropriate g-frame.Tue, 10 Jul 2018 19:30:00 +0100$C$-class functions and common fixed point theorems satisfying $\varphi $-weakly contractive ...
http://scma.maragheh.ac.ir/article_31846_0.html
In this paper, we discuss and extend some recent common fixed point results established by using $varphi-$weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a $C-$class function. Using $C-$class functions, we generalize some known fixed point results. This type of functions is a very important class of functions which contains almost all known type contraction starting from 1922. year, respectively from famous Banach contraction principle. Three common fixed point theorems for four mappings are presented. The obtained results generalizes several existing ones in literature.We finally propose three open problems.Sat, 14 Jul 2018 19:30:00 +0100