As we know, many existing numerical methods for solving nonlinear fractional time equations under propagation suffer from the phenomenon of decreasing convergence order.

  This

در اين پايان نامه، يك مدل شكارچي-شكار با دفاع القايي و بيماري در شكار كه از ديدگاه تكامل زيستي و اكو-اپيدميولوژي ساخته شده است، مورد مطالعه قرار مي‌گيرد. هدف اصلي اين پايان نامه بررسي تأثير بيماري بر پايداري جمعيت در مدل شكارچي-شكار با دفاع القايي است. ابتدا، مثبت بودن و كرانداري يكنواخت جواب‌هاي مدل اشاره شده اثبات مي‌شود. سپس، وجود و پايداري نقاط تعادل، بخصوص نقاط تعادل همزيستي شكار و شكارچي مورد مطالعه قرار مي‌گيرد. در اين مدل حداكثر نه نقطه تعادل وجود دارد. از يك تبديل پارامتري پيچيده براي بررسي ويژگي‌هاي نقاط تعادل همزيستي مدل استفاده مي‌كنيم. همچنين شرايط كافي براي وجود انشعاب هاپف بدست مي‌آيد. براي تحليل انشعاب هاپف و تعيين جهت سيكل‌هاي حدي در مدل شكارچي-شكار با دفاع القايي و بيماري، ضريب اول لياپانوف در مقادير بحراني پارامتر انشعاب محاسبه مي‌شود. در خاتمه شبيه‌سازي‌هاي عددي براي تكميل نتايج تحليلي انجام مي‌شود  

In this thesis, we focus on the Ekeland’s variational principle and some of its applications to equilibrium and quasi-equilibrium problems and existential results for equilibrium and Minty equilibrium problems. First, we state the Ekeland’s variational principle and then, using it, we present equilibrium forms of the Ekeland’s variational principle for cyclically antimonotone and cyclically monotone functions, and using these equilibrium forms, we present two existence theorems for equilibrium and Minty equilibrium problems, respectively. We also state an existence theorem for the quasiequilibrium problem using the Ekeland’s variational principle. Next, we study the existence of solutions for equilibrium and Minty equilibrium problems and then the relationship between them. It should be noted that with different assumptions such as the Minty lemma, cyclically monotonicity and cyclically antimonotonicity, we will study this relationship in topological spaces, topological vector spaces, and Banach spaces.   

We study a multi-group SAIRS-type epidemic model with vaccination. the role of asymptomatic and symptomatic infectious individuals is explicitly considered in the transmission pattern of the disease among the groups in which the population is divided. This is a natural extension of the homogeneous mixing SAIRS model with vaccination studied in Ottaviano et. al(2021) to a network of communities. We provide a global stability analysis for the model. We determine the value of the basic reproduction number R0 and prove that the disease-free equilibrium is globally asymptotically stable if R0<1. In the case of the SAIRS model without vaccination, we prove the global asymptotic stability of the disease-free equilibrium also when R0=1. Moreover, if R0>1, the disease-free equilibrium is unstable and a unique equilibrium exists. First, we investigate the local asymptotic stability of the endemic equilibrium and subsequently its global stability, for two variations of the original model. Last, we provide numerical simulations to compare the epidemic spreading on different networks topologies. 

   In this thesise,we stady the commuting graph,the power graph and the enhance power graph of agroup G that are denoted respectively Com(G),Pow(G) .and EPow(G).Furthermor,we introduce a new graph that is called the deep commuting graph of the group G   The vertex set of these graphs are the element of G and two elements of G are joined in the deep commuting graph if the pre -image of these   .elements.commute in each central extension of G      It is proved that deep commuting graph of G is between the commuting graph and the enhance power gra ph.       :Key word   .Deep commuting,Schur multiplier,Central extensio  

   Today, the emergence of generative models based on machine learning has provided a significant reduction in the bit rate of speech codecs. However, in real conditions and in the presence of destructive factors such as noise and distortion, the above processes face serious problems, which is caused by the sensitivity of the maximum likelihood criterion to outliers, as well as the inefficiency of modeling the sum of independent signals with Autoregressive model is used. In this thesis, a method based on predicting variance regularization is introduced to reduce sensitivity to outliers and thus increase system performance. In addition, it is shown that noise reduction to remove unwanted signals can increase the performance significantly. Also, extensive objective evaluations will be presented, which show that the proposed system based on the generative model provides a new coding performance mode for real-time speech signals at 3 Kbit/s.

Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor   networks. Inthiset we study the notion of excess for woven frames and prove that any two frames in a separable Hilbert space that are woven have the same excess. We also show that every frame with a large class of duals is woven provided that its redundant elements have small enough norm. Also, we try to transfer the woven property from frames to their duals and vice versa. Finally, we look at which perturbations of dual frames preserve the woven property

  A PRACTICAL NUMERICAL APPROACH TO SOLVE A FRACTIONAL LOTKA-VOLTERRA POPULATION MODEL WHITH NON-SINGULAR AND SINGULAR KERNELS Thesis Title:

dimension frames.Keyword: Frame, Tight frame, Parseval frame, synthesis operator , Analysis operator, Frame operator, Dual frame, Span, Redundancy, Upper redundancy, Lower Redundancy, orthonormal basis

  In this thesis, we examine theorems about bifurcation from one-dimensional kernels and generalizations of the Crandell-Rabinowitz theorem. Next, using a bifurcation theorem from one dimensional kernels, the bifurcation in Activator-inhibitor systems are discussed. Also, the effect of nonlocal diffusion on bifurcations and the formation of spatially heterogeneous patterns in the case when the rate of dispersion of the inhibitor is small enough, is study. Unstable steady state solutions and existence of Turing instability for the mentioned nonlocal systems is investigated.

  AbstractOne of the important concepts from the point of view of theory and computation is the con-cept of proper efficiency in multi-objective optimization. On the other hand, in computationalprocesses, we usually obtain approximate solutions. Therefore, it is necessary to study the prop-erties of these types of solutions and approximate solutions to the related scalar problems to beexamined. Based on this, in this thesis, a generalization of the concept of proper efficiency forproblems with an infinite number of objective functions is investigated. It turns out that someresults for ordinary multi-objective problems cannot be generalized to these problems. In addition,some scalarization methods such as weighted sum and the Chebyshev method are presented re-lated to properly efficient solutions to these problems. In addition, a unified method based on thedirectional Pascoletti–Serafini approach is presented to find efficient, properly efficient, and weaklyefficient solutions as well as similar approximate solutions. In the analysis of these solutions, whilepresenting some characterizations, simple and implementable optimality conditions for efficient

   تعامل شكار-شكارچي يا منبع-مصرف كننده، اساسي ترين و مهم ترين فرآيند در پويايي جمعيت است. بسياري از گونه   ها، مانند گياهان تك باره و جانوران يك بار زا كه پس از زادآوري مي ميرند، داراي نسل هاي ناهمپوشان گسسته هستند و تولد آنها در فصول توليد مثل به طور منظم اتفاق مي افتد. فعل و انفعالات آنها با معادلات تفاضلي توصيف و يا به صورت نگاشت هاي زمان-گسسته فرموله مي شوند. در اين پايان نامه، انشعابات را در يك مدل شكار-شكارچي گسسته با تابع پاسخ غير يكنوا كه توسط تابع ساده شده هالينگ IV توصيف شده است، مطالعه مي كنيم. همچنين ثابت مي كنيم كه مدل فوق انشعاب هاي مختلفي از هم بعد 1 را نشان مي دهد، كه شامل انشعابات فولد، انشعاب ترا بحراني، انشعاب فليپ و انشعاب نيمارك-ساكر مي باشد، زيرا مقادير پارامترها متفاوت است. علاوه بر اين، وجود انشعاب بوگدانوف -تاكنز از هم بعد 2 را مشخص و عبارات تقريبي منحني هاي انشعاب را محاسبه مي كنيم شبيه سازي هاي عددي نيز دهد براي نشان دادن تحليل نظري ارائه شده اند اين نتايج نشان مي دهد كه انشعاب بوگدانوف-تاكنز از هم بعد 2 در تكيني تبهگن در هر سه نسخه زمان-پيوسته، زمان-گسسته و زمان-تاخيري از مدل شكار-شكارچي با تابع پاسخ غير يكنوا برقرار است.

  In this paper, an efficient numerical scheme is constructed for a generalized fractional subdiffusion problem using a newly proposed generalized weighted shifted Grünwald-Letnikov (gWSGL) approximation for the generalized fractional derivative. The solvability, stability and convergence of the numerical scheme are analyzed using the discrete energy method. It is proven that the temporal convergence order is 2 and this is the best result to date. Simulation is further carried out to demonstrate the accuracy of the proposed numerical scheme

In this Thesis, we propose a new numerical scheme for two-dimensional fractional sub-diffusion problems using non-polynomial spline. The solvability, stability and convergence of the proposed method are established using the well known discrete energy methodology. It is shown that the spatial convergence order is at least 4.5 which improves the best result achieved to date. We also carry out simulation to demonstrate the accuracy and efficiency of the proposed scheme and to compare with other methods.  

In this thesis, we have examined the necessary and sufficient conditions for a group ring to be weakly nil-neat.  The first chapter contains the primitive concepts and definitions. In the seconds chapter, we define nil-clean group ring and weakly nil-clean group ring. The main purpose of the third chapter is to examine the weakly nil-clean group ring.

  We study the relationship between depth and regularity of a homogeneous ideal I and those of (I, f ) and I : f , where f is a linear form or a monomial.

  AbstractIn this thesis we study a host-generalist parasitoid model with Holling II functional response where the generalistparasitoids are introduced to control the invasion of the hosts. It is shown that the model can undergo a sequence ofbifurcations including cusp, focus and elliptic types degenerate Bogdanov-Takens bifurcations of codimension three, and adegenerate Hopf bifurcation of codimension at most two as the parameters vary, and the model exhibits rich dynamics suchas the existence of multiple coexistent steady states, multiple coexistent periodic orbits, homoclinic orbits, etc. Moreover,there exists a critical value for the carrying capacity of generalist parasitoids such that: (i) when the carrying capacity ofthe generalist parasitoids is smaller than the critical value, the invading hosts can always persist despite of the predation bythe generalist parasitoids, i.e., the generalist parasitoids cannot control the invasion of hosts; (ii) when the carrying capacityof the generalist parasitoids is larger than the critical value, the invading hosts either tend to extinction or persist in theform of multiple coexistent steady states or multiple coexistent periodic orbits depending on the initial populations, i.e.,whether the invasion can be stopped and reversed by the generalist parasitoids depends on the initial populatio   (iii) inboth cases, the generalist parasitoids always persist. Numerical simulations are presented to illustrate the theoretical results.-parasitoid model; Bogdanov-Takens bifurcation; Hopf bifurcation; Invasion; PersistencKeywords:Hoste; Extinction.

In the thesis, we investigate the well-posedness for abstract Cauchy problems with finite delay. We also study asymptotically equivalence of evolution equations and delay evolution equations.

Two spectral conjugate gradient methods based on some quasi-newton equation

  ‎In addition to their applications in data communication and storage‎, ‎linear codes also have nice applications in combinatorics and cryptography‎. ‎As a special class of linear codes‎, ‎minimal linear codes have important applications in secret sharing and secure two-party computation‎. ‎Constructing minimal linear codes with new and desirable parameters has been an interesting research topic in coding theory and cryptography‎. ‎Ashikhmin and Barg showed that $\\frac{w_{\\min}}{w_{\\max}}>\\frac{q-1}{q}$ is a sufficient condition for a linear code over the finite field$F_q$ to be minimal‎, ‎where $q$ is a prime power‎, ‎$w_{\\min}$ and $w_{max}$ denote the minimum and maximum nonzero weights in the code‎, ‎respectively‎. ‎The first objective of this thesis is to present a sufficient and necessary condition for linear codes over finite fields to be minimal‎. ‎This condition enables us to‎ ‎obtain several infinite families of minimal linear codes with $\\frac{w_{\\min}}{w_{\\max}}\\leq \\frac{q-1}{q}$‎. ‎The second objective of this thesis is to construct infinite families of binary and ternary minimal linear codes‎, ‎violating Ashikhmin and Barg's condition‎. ‎The weight distributions of all these minimal linear codes are also determined‎.  

  In this thesis will first introduce the basic concepts of dynamical systems, differential equa- tions, Philips systems and Poincaré mapping. In chapter two presents a standard form that includes all possible configurations in planar linear systems, and it is shown that the exis- tence of a focus in one zone is sufficient to get three nested limit cycle, independently on the dynamicsoftheanotherlinearzone. Inchapterthree,adiscontinuousplanarpiecewiselinear differential system in R is assumed. if it has a center, real or virtual, then the discontinuous planar piecewise linear differential system having at most two limit cycles.

  دراين پايان نامه وجود جواب هاي ضعيف براي يك دستگاه معادلات كيرشهف كسري منفرد و ‎دسته‎ اي از معادلات كيرشهف كسري منفرد با توابع وزن داراي تغيير علامت، با استفاده از روش منيفلد نهاري مورد بررسي قرار مي گيرد. ‌‌‌‌‌‌‌‌‌براي اينكار متناظر با نقاط بحراني نگاشت هاي تاري، منيفلد نهاري به سه زيرمجموعه تقسيم مي شود. به علاوه ثابت مي شود تابعك انرژي روي منيفلد نهاري بازدارنده و از پايين كراندار است و مينيمم هاي موضعي روي منيفلد نهاري نقاط بحراني تابعك انرژي هستند. سپس با نشان دادن وجود دو مينيمم موضعي روي زير مجموعه هاي متناظر با نقاط ماكسيمم و مينيمم نگاشت هاي تاري، وجود دو نقطه بحراني براي تابعك انرژي اثبات خواهد شد.

an independent unified section.  

AbstractIn this thesis, first some definitionsand elementary concepts of analysis and fractional calculus are discussed.Then, by using various fixed point theorems,such as Banach, Krasnoseleskii, Schauder, Leray- Schauder, Leray-Schauder'sNonlinear Alternative and Avery-Peterson, the existence of positive solutionsfor a fractional boundary value problem with boundary conditions involvingReimann-Stieltjes integral is investigated.At the end, the existence anduniqueness of solutions for an integro-differential boundary value problem of Caputotype with nonlocal boundary conditions is studied.  

اخيرا يكي از موضوعات مورد علاقه رياضي­دانان، مطالعه معادلات ديفرانسيل ضربه­اي به خصوص با عملگرهاي مشتق كسري( مشتق كسري ريمان- ليوويل و كاپاتو) بوده است به منابع [3-4] رجوع شود. با وجود اين وجود مطالعات جزئي روي جواب، يكتايي جواب و پايداري جواب ها براي معادله ديفرانسيل كسري با مشتق هيلفر انجام گرفته است، زيرا كه مشتق كسري هيلفر شكل كلي تري از مشتقات كسري ريمان- ليوويل را ارائه كرده است كه به صورت خلاصه ميتوان آن را يك درونيابي بين مشتق كاپاتو و مشتق ريمان- ليوويل فرض كرد. حال در اين پايان نامه، وجود جواب و پايداري معادلات ديفرانسيل كسري ضربه اي با عملگر مشتق كسري هيلفر مورد مطالعه و بررسي قرار خواهد گرفت.

در اين پايان نامه وجود جواب معادلات ديفرانسيل كسري انتقال-انتشار با استفاده آناليز غير خطي، روش هاي تغييراتي و قضيه گذرگاه كوهستاني بررسي مي شود

  AbstractIn this thesis, we investigate the existence of two nontrivial solutions in weighted Sobolev spaces, for a class of fourth-order elliptic equations, with assuming that, nonlinear parts is continuous with a quasicritical growth and it’s potential vanish at infinity, byusingthevariationalmethodandMountainPassTheorem. Therefore, we study the existence of two nontrivial solutions for fourth-order elliptic equations by settingtheAmbrosetti-Rabinwitsconditiononnonlinearpartsandsteepedpotential, by utilizing critical point theory, Mountain Pass Theorem and local minimization. Finally, as an application we will make report the similar results and cocentration phenomenona for second elliptic equations with concave and convex nonlinearities. Keyword: Fourth-order elliptic equation, Mixed nonlinearity, Variational method, cocentration phenomenona, concave-convex nonlinearity, quasicritical growth .

In this thesis, first we examine the existence of a sequence of weak solution for the non-local equation of the following fraction\\\\ ‎‎\\begin{cases}‎‎‎M\\Big(\\iint‎‎‎‎_{\\mathbb{R}^{2N}}\\frac{\\vert u(x)‎ -u (y)\\vert^{p}}{\\vert x‎ - ‎y\\vert^{N+ps}}dxdy\\Big)‎(-\\Delta)_{p} ‎^{s}u(x)=f(x,u)‎\\qquad‎\\qquad ‎in‎\\qquad‎\\Omega,\\\\‎  ‎‎‎ ‎u=0‎\\qquad‎\\qquad‎\\qquad‎\\qquad‎\\qquad‎\\qquad‎\\qquad‎\\qquad‎‎\\qquad‎‎\\qquad‎ ‎in‎\\qquad‎‎‎\\mathbb{R‎^{N}‎}‎‎\\backslash\\Omega, ‎‎‎\\end{cases}‎‎‎‎\\\\‎where ‎$ ‎\\Omega ‎$‎ ‎is ‎an ‎open ‎bounded ‎subset ‎of‎ ‎$ ‎\\mathbb{R‎^{N}‎} ‎$‎ ‎with ‎Lipshcitz ‎boundary‎ ‎$ ‎\\partial‎\\Omega‎ $‎,‎‎ ‎$ (-‎\\Delta)‎_{p}‎^{s}‎‎‎ $ ‎is ‎the ‎fractional ‎p-Laplacian ‎operator ‎with‎ ‎$ 0<  lt;1<  lt;N $ ‎such ‎that ‎‎‎$   lt;N $‎,‎‎ ‎‎$ M $ ‎is a‎ ‎continuous ‎function ‎and‎ ‎$ f $ ‎is a ‎‎Carat‎‎heodory ‎function ‎satisfying ‎the ‎Ambrosetti-Rabinowitz-type ‎condition‎. When ‎$ f $ ‎satisfies ‎the ‎suplinear ‎growth ‎condition,we ‎obtain ‎the‎ existence of a sequence of nontrivial solutions by using the symmetric mountan pass theorem; when ‎$ f $ ‎satisfies ‎the ‎sublinear ‎growth ‎condition, ‎we ‎obtain ‎infinitely ‎many ‎pairs ‎of ‎nontrivial ‎solutions ‎by ‎applying ‎the ‎Krasnoselskii ‎genus ‎theory. ‎Our ‎results ‎cover ‎the ‎degenerate ‎case ‎in ‎the ‎fractional ‎setting: ‎the ‎Kirchhoff ‎function‎ ‎$ M $ can be zero at zero. ‎Using Mountain pass theorem we prove the existence of infinitely many solutions for the above problem. Then we discuss the existence of infinitely many solutions for fractional equations with sign changing nonlinear terms via varational methods in fact if the nonlinear terms are sign changing and satisfy p-supper growth, we obtain the existence of infinitely many solutions for boundary value problems driven by fractional p-Laplacian.‎‎‎‎‎‎‎‎‎‎\\\\‎‎\\textbf{Keywords:} \\\\‎‎\\textit{Fractinal p-Laplacian‎, Kirchhoff problems‎, Differential operator‎, Mountain pass Theorem‎, Nonlocal operator‎, Variational methods‎, Weak solution‎ }‎\\end{latin}‎

  Today, air pollution has become one of the serious concerns of humankind, and it has become more and more visible to the researchers and the owners of this science, since this disruption directly affects and affects human health. We know that suspended particles have a wide range of sizes and sources. In this study, the SMPS suspended particle measurement system was used to examine the particle size distribution in various environments.

Firstly we explore some properties of K-frame  in terms of decompositions of operators. Then we  pay more attention to characterize the dual K-Bessel sequences of a given K-frames.                                                                                  

‎In‎ this thesis, we consider the multiplicity and existence of solutions for some kirchhoff-type equations by variational method and critical point theory.Also, we have studied the existence of positive solutions for some partial differential equations.

  ‎In this thesis‎, ‎using variational methods‎, ‎the existence of weak solutions for two margin-top:0px; margin-bottom:0px; margin-left:0px; margin-right:0px; -qt-block-indent:0; text-indent:0px; -qt-user-state:0;">‎For this purpose‎, ‎using certain conditions‎, ‎it is proved that the energy functional satisfies the Palais-Smale condition‎. ‎Then‎, ‎using the Ambrosetti-Rabinowitz condition and the symmetric Mountain Pass Theorem‎, ‎the existance of two nontrivial solutions for the considered equation is proved‎. ‎Also‎, ‎using Lions theorem‎, ‎the concentration of solutions‎, ‎is investigated‎. ‎As an application of the obtained results‎, ‎the existence and concentration of solutions to an elliptic equation with convex-concave nonlinearity is established‎. ‎Finally‎, ‎using the symmetric Mountain Pass Theorem‎, ‎the existence of infinitely many weak solutions to a system of Schrodinger–Kirchhoff equations of fourth-order is investigated

  In this thesis, the existence of weak solutions to a franctional system of p-Laplacianequations and a singular p-Laplacian equation with sing-changing functions, is investigatedvia the Nehari manifold method. To do this, corresponding to critical pointsof fibering maps, the Nehari manifold is divided into three sets. Moreove is provedthat the energy functional is coercive and bounded from below on the Nehari manifoldand local minima on the Nehari manifold are critical points of the energy functional.Then by showing the existence of two minima on the subsets of Nehari manifoldcorrespanding to maxima and minima of fibering maps, the existence of two criticalpoints of the energy functional will be proved.

 complex linear systems have many applications in scientific computing and applied engineering most of these equations don't have exact solution.therefore the main purpose of this thesis is to obtain some numerical methods for solving these equations.by obtaining the spectral radius of the introduced method,their convergence analysis will beinvestigated.finally by some numerical examples efficiencity of the methods will be explained

This research speaks about three spline subjects, rstly quadratic b-spline which was used to reconstructan approximating function by using three parameters for that, second a trigonometric spline which wasconstructed by a trigonometric functions mainly to build an approximating function as we will see inmuch details and lastly, quintic b-spline which was used to construct an interpolation method, we willsee in detailed explanations how they have been used and how were the nal results found. Also, wehave demonstrated some examples of error analysis estimations and a comparison with other previousworks, to see which one is better and easier, de nitions are provided with theories and methods toexplain every single step in this work, and an overview of the theories of interpolations for those splinesand their applications in numerical analysis. At the end, the researcher wanted to say that it has beenspoken about cubic spline interpolation in details because its the main spline that is used in our currenttime, and the illustrated examples were of Matlab and Mathematica simulation programs.

در اين پايان نامه كرانداري وفشردگي عملگرهاي انتگرال ريمان-ليوويل روي فضاهاي موري را بررسي مي كنيم0مشخصه سازي جواب براي معادله انتگرال آبل بدست اورده وباكمك نتايج قضيه نقطه ثابت وجوديكتايي جواب براي مسئله كوشي ثابت خواهد شد  

   In this thesis first the existence and multiplicity of positive solutions for a class of Kirchhoff type equations with concav and convex nonlinearities are investi- gated. Next, the existence of positive solutions for a class of Kirchhoff type equations involving a crieical growth nonlinearity is studied. To prove the mentivned results, the Nehari manifold method and the Ekland Variational Principle are used. First it is proved that local minima of the energy functional are critical points of the energy functional. Next using critical points of fibring maps, the nehari manifold is divided into three sets, and it is shown that the energy functional has two local minima in these sets.

  ‎This thesis examines the Turing patterns in the Gierer–Meinhardt models‎. ‎The stability of equilibrium points in a system without diffusion is studied‎. ‎Moreover‎, ‎the suficient condition for this system to have Hopf bifurcation is carefully stuided‎. ‎By adding diffusion terms it is shown that‎, ‎influenced by different diffusion coefficients‎, ‎both the stable equilibrium and the bifurcated limit cycle of the Hopf bifurcation are affected by the Turing instability‎. ‎Besides‎, ‎in each case‎, ‎Turings conditions of instability are presented‎.

  This thesis concerns the stability and bifurcations in two planer systems of ODE’s,which are models of a prey - predator system and a SIR epidemic model.It is proved that the predator - prey model exhibits several bifurcations.These bifurcations are ecologically important and the saddle - node bifurcation andcodimension 2 Bogdanov - Takens bifurcation especially will lead to the potentiallydramatic variation of the system dynames.In the SIR model, it is proved that under some conditions the system exhibits backward bifurcation and Hopf birfurcation.

In this thesis first, some concepts and theorems of sobolev space are explianed.Then the existence of nontrivial wenk solutions for a class of quasilinear Schrodinger

  In this thesis, first the definition and elementary concepts of analysis and fractionalcalculus is discussed.Then, by using a various fixed point theorems, such as Banach, Krasnoseleskii, Nonlinearcontractions, Leray-schauder Nonlinear Alternative and Leray-schauder degree,the existence and uniqueness of the solutions for a fractional boundary value probleminvolving Erdelyi-Kober operator is investigated.At the end, by using the conception of measures of noncompactness and the Darbotheorem, the existence of a solution for a >involving Erdelyi-Kober operator is discussed.

بررسي كنترل در فضاهاي هيلبرت

در اين پايان نامه نخست مفهوم انتگرال كسري ريمانليويل وانتگرال كسري اردلي كوبر بيان مي گردد در ادامه وجود جواب هاب معادلات ديفرانسيل كسري با استفاده از قضاياي نقطه ثابت را بررسي مي كنيم

  In this thesis ‎we‎ generalize the notion of ‎$n$‎‎-weak module amenability of ‎$A$‎‎ which is a Banach module over another Banach ‎algebra‎ ‎$U$‎‎ ‎with‎ compatible actions to that ‎of‎ ‎‎‎‎‎$‎(\\sigma)$‎-‎‎‎$n$‎‎-‎weak‎ module amenability ‎for‎ ‎$n\\in‎ ‎‎\\mathbb{N}$‎‎‎ ‎and‎‎ ‎$\\sigma\\in‎ ‎‎Hom_{U}(A)‎$‎‏ ‎.‎We also investigate the relation between this new concept of amenability of ‎$A$‎‎ and the quotient Banach algebra ‎$‎‎A/‎J$‎‎ where ‎$J$‎‎ is the closed ideal of ‎$A$‎‎ generated by elements of the ‎form‎ ‎‎‎$‎‎(a.‎‎\\alpha‎)b -‎‎‎ a(\\alpha.‎‎b)$‎‎‎ ‎for‎‎ ‎$a‎,‎b\\in‎ ‎A$‎‎‎ ‎and‎‎ ‎$\\alpha‎‎ ‎\\in‎‎‎ ‎U$‎‎‎‎ ‎.‎As a consequence ,we show that the semigroup ‎algebra‎ ‎‎‎$‎l‎^{1}(S)‎$‎‎ is ‎$‎‎(\\sigma‎)‎$-‎‎‎‎$‎(‎2n+‎‎‎1)‎‎$-‎weakly module ‎amenable‎ as an ‎‎$‎l^{1}(E)‎$‎ -module for each $‎n\\in \\mathbb{N}‎$‎‎‏ ‎and‎ $‎‎‎‎\\sigma ‎\\in ‎‎‎‎Hom_{l^{1}(E)‎}(‎l‎^{1}(S)‎)‎$‎‎‎ where ‎‎‎$‎S‎$‎ is an inverse semigroup with the set of idempotents ‎‎‎$‎E‎$‎

  در سالهاي اخير متيو فضاهاي متريك جزيي وشبه متريك و شبه متريك وزن دار را معرفي كرد . ايشان به ارتباط بين آنها پرداخت وبيان كرد كه تحت چه شرايطي ميتوان فضاي متريك جزيي وشبه متريك را يه يك متر تبديل كرد. يكي از اهداف پايان نامه اين است كه با استفاده از يك نوع خاص از انقباض ضعيف معرفي شده توسط چريچ وبا كمك گرفتن از توابع كنترل ناپيوسته قضييه نقطه ثابت باناخ را به فضاهاي متريك جزيي گسترش  مي دهيم.

  ‎In ‎this ‎theisi ‎we ‎invsestiyqte ‎on ‎concept ‎of ‎operator‎-‎valued frames.‎‎In ‎fact, ‎operator-‎‎valued ‎(or g‎-‎‎frames) ‎are ‎generalization‎s of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and mor. In this article , we give a new formula for operator-valued frames for finite dimensional Hilbert spaces. As an application, we derive in a simple manner a recent result of A. Najati conceerning the approximation of g-frames by Parseval ones. we obtain also some results concerning the best approximation of operator-valued frames by its alternate dual, with optimal estimate.

  The dynamics of a general di?usive predator–prey system is considered. Existence and nonexistence of non-constant positive steady state solutions are shown to iden- tify the ranges of parameters of spatial pattern formation. Bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as non-constant steady state solutions are studied. Keywords: Reactiondi?usion; Patternformation; Globalbifurcation; Predatorprey; StrongAllee e?ect; Spatiotemporal patterns

‎In this thesis‎, ‎we compare the abelian subalgebras and ideals of maximal‎‎dimension in some 0px; MARGIN: 0px; -qt-block-indent: 0; -qt-user-state: 0">‎abelian subalgebras of solvable Lie algebras and study the 0px; MARGIN: 0px; -qt-block-indent: 0; -qt-user-state: 0">‎an abelian subalgebra of codimension 2‎. ‎Also‎, ‎we prove that nilpotent Lie algebras with‎‎an abelian subalgebra of codimension 1,2 or 3 contain an abelian ideal with the same dimension‎.‎Furthermore‎, ‎we investigate‎ ‎the structure of Lie algebras with a core-free‎ ‎maximal subalgebra and use them to introduce the conceptes of crown and pre-crown for chief factors‎.

  In this thesis we consier tree concepts of orthogonlity in a Hilbert C?-module V over a C?-algebra A : the Birkhof-James orthogonality ?B , the strong Birkhof-ames orthogonlity ?SB , and the orthogonality with respect to the A-valued inner product on V . We characterize the classes of Hilbert C?-modules in which any two of them coincide .

در اين پايان نامه مفاهيم بهينگي سره در بهينه سازي برداري با ساختارهاي ترتيبي متغير معرفي شده و با استفاده از برخي روشهاي اسكالرسازي جديد خواص مشخصه مختلفي براي تشخيص عناصر كاراي سره ارائه مي شود. اين اسكالرسازي ها براساس تابعكهايي تعريف ميشوند كه از عناصر مخروط دوگان افزوده، بدست مي آيند. ضمن بررسي رابطه ي بين مخروطهاي دوگان افزوده و مخروطهاي بيشاپ-فلپس، خواص اين تابعكها مورد مطالعه قرار ميگيرد. همچنين خواص مشخصه اي براي ديگر مفاهيم بهينگي مانند عناصر بهينه ضعيف و بهينه قوي بدست مي آيد..

In this thesis, we study the fractional calculus and fractional differential equations with Hadamard derivatives, and includes the following parts: in the first chapter, some properties, definitions and theorems of fractional calculus, nonlinear Analysis and fixed point theorems to be introduced that will be used to prove our main results. In the second chapter, the existence and unique   of solutions for a system of Hadamard type fractional differential equations is derived from Leray-Schauders and fixed point theorems guards will be examined. In the next chapter, the existence and uniqueness of solutions ‎using Banachs fixed point theorem for fractional impulsive equations with Hadamard derivatives studied is derived. in the end chapter, existence of solutions for fractional differential equations involving the Hadamard derivatives studied is derivedKeywordsFractional differential, Hadamard fractional derivatives‎, ‎Banachs-fixed point theorem‎, Leray- Schauders theorem‎, Existence of solutions ‎

  In thesis propose nonpolinomial spline and Hermit nonpolynomial spline interpolation and present method to determine optimal value of parametrs which generate minimum error in approximation and used of functions interpolation such the Fouer Series and the Hermite nonpolynomial cubic spline and nonpolynomial cobic spline and interpolated functions for example Runge s Phenomenon Numerical simulations are carried out for the analisis of error in cubic spline and nonpolynomial interpolations.   In this thesis non-polynomial spline for the numerical solution of two-point boundary value problems and singularly perturbed boundary value problems are studied.And it is reduced to sixth order of non-polynomial spline that is used for solving boundary value of second order singularly perturbed.in addition to in both groups of problems, errors and convergence are analyzed.The numerical example are given to illustrate the efficiency of proposed methods.

  ‎In‎ ‎this‎‎ ‎thesis‎,‎‎ ‎first‎‎ ‎we‎‎ ‎investigate‎,‎ ‎the‎‎ ‎existense‎‎ ‎and‎‎ ‎multiplicity‎‎ ‎o‎‎f‎ ‎positive‎‎ ‎solutions‎‎ ‎to‎‎ ‎an‎ ‎N-‎Laplacian‎‎ ‎equation‎‎ ‎in‎‎‎ ‎$ ‎\\mathbb{R}^{N‎‎}‎‎‎ $‎ ‎with‎‎ ‎singular‎‎ ‎and‎‎ ‎exponential‎‎ ‎nonlinearity‎.‎ ‎To‎‎ ‎do‎‎ ‎this‎,‎ ‎we‎‎ ‎use‎‎ ‎the‎‎ ‎Nehari‎‎ ‎manifold‎ ‎method‎.‎ ‎First‎‎, ‎we‎‎ ‎prove‎‎ ‎that‎‎ ‎‎‎local‎‎‎ ‎minima‎‎ ‎of‎‎ ‎the‎‎‎ ‎energy‎ ‎functional‎‎ ‎i‎n‎‎ ‎the‎‎ ‎Nehari‎‎ ‎manifold‎‎ ‎are‎ ‎critical‎‎ ‎‎points‎‎.‎Then‎ ‎we‎‎ ‎divide‎‎ ‎the‎‎ ‎Nehari‎‎ ‎manifold‎‎ ‎in‎‎to‎‎ ‎three‎‎ ‎sets‎‎ ‎corresponding‎‎ ‎to‎‎ ‎local‎‎ ‎maxima‎‎, ‎local‎‎ ‎minima‎‎ ‎and‎‎ ‎points‎‎ ‎of‎‎ ‎inflection‎‎ ‎of‎‎ ‎fibering‎‎ ‎‎maps,‎‎‎ ‎and‎‎ ‎we‎‎ ‎‎find‎‎‎ ‎local‎‎ ‎minima‎‎ ‎of‎‎ ‎‎ ‎the‎‎‎ ‎energy‎ ‎functional‎ ‎in‎‎ ‎these‎‎‎‎ ‎sets‎.‎ ‎In‎‎ ‎the‎‎ ‎next‎‎ ‎part‎‎‎ ‎of‎‎ ‎this‎‎ ‎thesis‎,‎ ‎we‎‎ ‎study‎‎ ‎the‎‎ ‎existence‎‎ ‎of‎‎ ‎a‎ ‎nontrivial‎‎ ‎solution‎‎ ‎for‎‎ ‎a system‎‎ ‎of‎‎ ‎p‎‎-‎Laplacian‎‎‎ ‎equation‎‎ ‎in‎‎ ‎a‎ ‎bounded‎‎ ‎domain‎‎ ‎and‎‎ ‎under‎‎ ‎the‎‎ ‎Dirichlet‎‎‎ ‎bounda‎ry‎‎ ‎condition‎.‎ ‎For‎‎ ‎this‎‎ ‎problem‎‎‎ ‎we‎‎ ‎prove‎‎ ‎that‎‎‎‎ ‎the‎‎‎ ‎energy‎ ‎functional‎ ‎has‎‎ ‎the‎‎ ‎geometry‎‎ ‎of‎‎ ‎mountain‎ ‎pass‎‎. ‎Then‎‎‎‎ ‎using‎‎ ‎the‎‎ ‎S‎addle‎ ‎P‎oint‎‎ ‎Theorem‎‎‎‎ ‎of‎‎ ‎Rabinowitz‎‎‎‎ ‎and‎‎ ‎a‎ ‎generalization‎‎ ‎of‎‎ ‎the‎‎ ‎Landesman‎-‎Lazer‎‎ ‎condition‎,‎ ‎the‎‎ ‎existence‎‎ ‎of‎‎ ‎a‎‎ ‎nontrivial‎‎ ‎solution‎‎ ‎is‎‎ ‎proved‎.‎

  In this thesis, we investigate the existence of weak sloutions for Schrodinger-Poisson systems. First, we study the existence and multiplicity of solutions for a weighed system of Schrodinger-Poisson with a sign-changing weigh in R 3 . To do this, we use the Nehari manifold and concentration compactness principle. In this part, we prove that local minima of the energy functional are weak solutions of the mentioned Schrodinger-Poisson system. In the next part of the thesis, we study the existence of a ground state solution for an asymptotiocally periodic critical growthm in R 3 . In this problem, to overcome the loss of compactness and unboundedness of the energy functional, on the whole space H 1 (R 3 ), we use the Nehari manifold and the concentration compactness principle.

  This thesis is devoted to study the number of limit cycles bifurcated from the periodannulus of two polynomial vector fields, under polynomial perturbative of degree n.The analysis is carried out by estimatry the number of zeroes of the correspondingAbelian integrals and averaged function. Chebeyshev criterion is one of the toolsfor deriving sharp upper bound for the number of zeroes of the Abelian integrals.Moreover, the distribution of the bifurcated limit cycles is also considere:

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