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.   

Nonparametric methods constitute a highly significant > To address this issue, in 2016, Morovati et al. proposed a generalization of Barzilai-Borwein methods for multi-objective optimization problems. Compared to other gradient-based methods, their approach demonstrated notably higher accuracy and speed, which drew significant interest from researchers in this area. More recently, another generalization of the Barzilai-Borwein method has been introduced, in which a specific weight is assigned to each objective function. The aim of assigning these weights is to reduce the adverse effect of conflicts among objectives on the step size reduction. The authors of the respective study compared their proposed method with that of Morovati et al., and their analysis and numerical results state that their proposed approach has substantial superiority. However, in this thesis, this issue is investigated more critically and thoroughly. It is demonstrated that the above-mentioned analysis is based on a form of false convergence for the newly proposed method and an improper comparison between the two approaches. In fact, it is shown that, contrary to the claims in the literature, the method of Morovati et al. has significant advantages over the proposed approach. This superiority is confirmed both on the test problems presented in the prior study and on a much broader set of ‎benchmark‎  

Let $R$ be a commutative, Noetherian, Local ring and $\\mathfrak{a}$ , $\\mathfrak{b}$ are parameters ideals of $R$ such that $\\mathfrak{a}\\subseteq\\mathfrak{b}.$ thus $\\Hom_R(R/\\mathfrak{a},R/\\mathfrak{b})$ is a free module over $R/\\mathfrak{a}$ of rank one.Now let $M$ be a finited generated $R$-module. in this work, we study the structure of such modules of homomorphisms $\\Hom_R(R/\\mathfrak{a},M/\\mathfrak{b}M)$ that $M$ is not Cohen-Macaulay. Our main Results start with small dimension then we generalize to higher dimensions.\\textbf{Keywords}:\\textit{System of parameters, Depth, Dimension, Cohen-Macaulay, Parameter ideal, Indecomposable module, Torsion submodule, Torsion functor}  

  In this research, a numerical method based on B-spline functions has been developed to solve a set of linear and non-singular singular and non-singular fractional boundary value problems. The approximate solution will be determined by discretizing the main problem with the help of B-spline function in uniform grid points. The convergence analysis of the method is investigated through the matrix approach. Linear and non-linear examples are considered to demonstrate the accuracy and efficiency of the method. The proposed method provides a second-order approximation to solve the investigated problem. This method provides much more accurate results at a lower cost. That is, the cubic spline method with a uniform step length has a lower computational cost. Another advantage of this research is that single points do not appear in the derivative of the fraction.

   As an extension of the 2D fractional Fourier transform (FRFT) and a special case of the 2D linear canonical transform (LCT), the gyrator transform was introduced to produce rotations in twisted space/spatial-frequency planes. It is a useful tool in optics, signal processing and image processing. In this thesis, we study discrete gyrator transforms (DGTs) based on the 2D LCT. Taking the advantage of the additivity property of the 2D LCT, we introduce three kinds of DGTs, each of which is a cascade of low-complexity operators. These DGTs have different constraints, characteristics, and properties, and are realized by different computational algorithms. Besides, we introduce a kind of DGT based on the eigenfunctions of the gyrator transform. This DGT is an orthonormal transform, and thus its comprehensive properties, especially the additivity property, make it more useful in many applications. We also develop an efficient computational algorithm to significantly reduce the complexity of this DGT.

In this thesis, we study the theory of the (a,k)-regularized resolvent families on a Banachspace. Thesefamiliesincludewell-knowclasses,suchasC0-semigroups,cosine and resolvent families of bounded linear operators. Inparticular,weprovide new insights on the structural properties of the theories of C0-semigroups, strongly continuous cosine families and ?-resolvent families. Key words: one parameter families of bounded operator, C0-semigroups, Cosine families, (?,?)resolvent families, (a,k)-regularized resolvent family, one-zero law.

In this thesis a representation of continuous functions is presented and then the Reisz representation theorem by using equilibrium problem is investigated.

In this thesis, based on W.K. Zahra, S.M. Elkholy and M. Fahmy (2019) [53], anefficient numerical method is introduced for solving the time-fractional Swift–Hohenberg equation in the sense of Riemann–Liouville derivative. Using rational spline function and nonstandard finite difference technique, numericalmethod is introduced for approximations Swift–Hohenberg. Using the Fourierseries, the method is convergent and unconditionally stable. Also, investigatedthe existence and uniqueness of the proposed method. At the end numericalresults are demonstrated to validate the applicability and the theoretical results.

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.

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.  

In this thesis, we consider astrongly continuous cosine family {C(t)}t?0 on a Banach space, and prove that the condition lim t?0+ sup ? C(t) ? I ?< 2 implies that C(t) converges to I in the operator norm. we further prove that the stronger assumption supt?0 ? C(t) ? I ?< 2 yields that C(t) = I for all t ? 0. For discrete cosine functions, the assumption sup n?N ? C(n) ? I ? ? r < 3 2 yields that C(n) = I for all n ? N. Furtheremore, we find a discrete cosine family that shows for r ? 3 2 , this conclusion does no longer hold. Morevoer, from the estimate sup t?0 ? C(t) ? cos(at)I ?< 1 we conclude that C(t) equals cos(at)I.   

  Quasi-newton methods are an important class of iterative methods for solving unconstrained optimization.These methods can be used when the Hessian matrix is difficult or time consuming to eraluate. Insted of using an estimate of the Hessian matrix, these methods buildup an approximate Hessian matrix by using gradient information. This family is one of the popular algorithms and has many advantages, but there are some drawbacks on them. This methods only use the gradient valuse and don't use the function valuse.Also, in most cases, the quasi newton method can't guarantee the positive definite of Hessian matrix.The modified quasi-newton methods suggest some proposals to overcoming this disadvantages.\\\\In this thesis, two new family of modified quasi-newton methods were investigated. firstly, a modified BFGS algorithm with global convergence properties for nonconvex functions were presented. In the second part by modifying the interpolation conditions to approximate the quadratic model of the function, a new modified quasi-newton equation is introduced. Based on this equation, a modified BFGS algorithm is presented.

This thesis examines of three chapters, which in the first chapter introduce the concepts that are needed, including KKM and generalized KKM which are tools for solving fixed-point problems.

در اين پايان نامه به بررسي مسئله ي تعادل عملگر تعميم يافته پرداخته شده است ودر ادامه مسئله ي شبه تعادل را مورد بررسي قرار داده وسپس كاربردهاي مسئله ي شبه تعادل در مسئله ي شبه بهينه سازي و مسئله ي نابرابري شبه تغييراتي ارايه شده است.

‎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.

  Using effective liquid drop model, we studied the proton radioactivity and alpha decay of some neutron deficient nuclei. For these nuclei the experimental half- lives are available. The purpose of this thesis is to calculate the half-lives of these decays based on the effective liquid drop model and competition between them. For som isotopes Ir and Au, the variations of half-lifves of these decays are plotted in terms of the neutron number. Also, for the proton radioactivity, we have obtained the variation of the reduced half-lives with Coulomb parameter. The reduced half-lives logarithm has a linear relation ship with this parameter. The obtained results of this model show that there is a good agreement between the experimental and theoretical results for the half-lives of the proton and alpha decay. Also, the dominant decay mode predicated by this model is in a agreement with the experimental results.

A J-frame for a Krein space H is in particular a frame for H (in the Hilbert space sense).But it is also compatible with the indefinite inner-product of H meaning that it determines a pair of maximal uniformly definite subspace.

  در اين پژوهش، فرآيند درج واترمارك شامل اعمال روش بهينه سازي هوشمند DE بر روي تصاوير ميزبان و واترمارك براي يافتن مكان مناسب هر بلوك از تصوير واترمارك در تصوير ميزبان است. سپس جهت بازيابي موفق،‌ خروجي برنامه بهينه سازي در تصوير ميزبان تحت حوزه فركانسي جاسازي مي­شود.   همچنين ضرايب مورد استفاده در جاسازي تصاوير به شكل بهينه بدست آمده است تا بيشترين مقدار   R را بدست دهد. در اين روش، يك بهينه سازي چند هدفه با استفاده از الگوريتم تفاضلي انجام شده است كه در آن مقدار   R در مرحله جاسازي براي تصوير واترمارك و در مرحله استخراج براي تصوير واترمارك بازيابي شده، بسيار مناسب است. در فرآيند درج و استخراج واترمارك، تعبيه و آشكارسازي واترمارك مهمترين بخش مي­باشند چرا كه مقاوم بودن طرح واترماركينگ به بخش تعبيه واترمارك مربوط مي­باشد. سپس مقاوم بودن طرح واترماركينگ در بخش نتايج تجربي مورد ارزيابي قرار مي گيرد و در بخش نتايج تجربي تصوير واترمارك شده را تحت حملاتي از قبيل فشرده سازي تصوير، نويز گوسي و غيره مورد آزمايش قرار داده   و صحت درستي وجود واترمارك مورد ارزيابي قرار خواهد گرفت.

   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.

در اين پايان نامه بررسي ارتباط جواب هاي كارا و كاراي ضعيف از مساله بهينه سازي برداري با استفاده از توابع اسكالر ساز مي پردازد 

Banachs fixed point is one of the main fields of research in non-linear analysis of analysis, and is the first to be described in the Banach Rescort. This case has been considered by many researchers for its application and its simplicity, which has been generalized in various ways, such as weakening the contraction inequality, weakening the topology of space, and so on.‎‎‎‎‎This thesis consists of three chapters. In the first chapter, the definitions and the necessary theorems are expressed. The second chapter of this thesis is titled as the fixed point for a weak contraction, which deals with the articles of Chric, Zhang, and Sang, which are presented in full metric space. We also consider the Suzuki case, which is an extension of the Banach contraction theorem, and its generalization‎. We also provide examples and applications of these cases, which will make the results clearer. The third chapter includes  F ‎-‎weak contraction and some of its results. Then we will generalize the contraction of the Banach using the functions called the auxiliary functions introduced by Matkawski and known as the  \\ varphi ‎-‎contraction. We also consider a new type of weak mapping called  F ‎‎-‎‎‎contraction introduced by Imovsky. In this chapter we study the contraction of fixed point theorems for the mapping f using the  F ‎‎-contraction and then the applications of the theorems obtained in the fractal theory are presented.

In this thesis, we study numerical schems for solving American put option pricing problem and for this purpose present efficient numerical methods. Unlike an European option, the value of an American option satisfies in a linear complementarity problem. We first approximate the linear complementarityproblemwithanonlinearfractionalpartialdifferentialequationbyapenaltyterm, thenweobtainsolutionsofthisequationbyFiniteDifferenceMethodandfinallywestudyanother linear complementarity problem by Laplace Transform Method and Finite Difference Method, and compare these methods by giving examples. So the purpose of this thesis is to provide methods for American put option pricing.   

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

پايان نامه ارشد(6واحدي)

  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.

One of the most important subjects that matters to either government organization and non-government specially for Judicial, security and law enforcement systems is preventing forgery, Undoubtedly, in order to prevent, it is necessary to take this issue into the account. As the field of knowledge and technology progressing, the methods of committing crime are also evolving in various dimensions and levels. Therefore, obtaining effective results in the prevention of documents forgery requires the application of indicators and security components in documents as well as utilizing modern technologies in the prevention and protection of documents forgery. Establish bank checks in a digital and secure way, and preventing counterfeiting of information, faces two major challenges including error and security. In this thesis, by implementation of digital signature based on elliptical curves all check data is generated from this type of signature, tended to keep information safe and secure by appointing this signature as resistant watermarking to the blue component of the image and DTC middle frequencies domain. Even though, AES cryptography and logistic mapping are used to increase the security of cache information.Besides, the inclusion of fragile cryptographic information and reconstruction of this information to investigate the non-manipulation of the red component of the image by encryption and decryption elliptical curve in the spatial domain being concluded.‎ While data transferring, due to the noise and interference, the data can be subjected to be incorrect. In this thesis applying codes‎ BCH(31‎, ‎16)it is possible to correct up to three possible errors. ‎The production of digital signature is done applying the software of ‎SAGE‎ and the placement of the information cryptography and reconstruction of this information is implemented by MATLAB software.

  A trust-region-based algorithm for the nonconvex unconstrained multiobjective optimization problem is considered. It is a generalization of the algorithm proposed by Fliege et al. for convex problems. Similarly to the scalar case, at each iteration a subproblem is solved and the step needs to be evaluated. Therefore, the notions of decrease condition and of predicted reduction are adapted to the vectorial case. A rule to update the trust region radius is introduced. Under differentiability assump- tions, the algorithm converges to points satisfying a necessary condition for Pareto points and, in the convex case, to a Pareto points satisfying necessary and sufficient conditions. Furthermore, it is proved that the algorithm displays a q-quadratic rate of convergence. The global behavior of the algorithm is shown in the numerical ex- perience reported. Keyword: Multicriteria optimization, Multiobjective programming, Pareto points, Newton’s method ,Trust region.

  آنچه بهينه‌سازي را از كاربردهاي عملي دور نموده است ناشي از دو واقعيت عملي مهم است. يكي تنوع اهداف و معيارهاست كه در بيشتر موارد در تضاد و تقابل با يكديگرند و ديگري نادقيق بودن داده‌هاي اوليه است. براي رويارويي با اين چالش مفهوم پايداري در بهينه‌سازي چندهدفه ارائه شد كه مورد بحث اين پايان‌نامه است.  در اين پايان‌نامه، مفهوم پايداري از مسائل تك‌هدفه به مسائل چندهدفه تعميم داده مي‌شود. منظور از جواب پايدار جوابي است كه به‌ازاي تمام سناريوهاي ممكن كارا بماند. همچنين مفهوم پايداري مينماكس مورد مطالعه قرار مي‌گيرد. فرآيند ارائه شده در اين زمينه، تركيبي است از پايداري در مسائل تك‌هدفه و بهينه‌سازي چندهدفه معين. به‌طور خاص در مسائل بهينه‌سازي چندهدفه‌ي خطي، فرمولي براي شعاع پايداري شدني و شرايط بهينگي قابل اجرا براي جواب‌هاي كاراي ضعيف پايدار ارائه مي‌شود. ضمن معرفي جواب‌هاي كاراي ضعيف بسيار پايدار يك فرآيند محاسباتي نيز براي محاسبه‌ي اين جواب‌ها بررسي مي‌شود. سرانجام يك فرآيند بهينه‌سازي دوهدفه براي تقليل مرز كارا و كمك به تصميم‌گيرنده جهت اتخاذ تصميمي ارجح ارائه مي‌شود. در اين راستا، پايداري جواب و پايداري مدل مطرح مي‌شود. الگوريتم‌هاي محاسباتي مربوطه در اين زمينه براساس تجزيه‌ي وجهي است.

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 ‎