يك خانواده مهم از اين اصلاحات روش هاي گراديان با تآخيرمي باشد. روش هاي گراديان با تاخير (GMR) يك روش تكراري غير يكنوا است كه براي حل معادلات خزي بزرگ متقارن و همچنين معين مثبت توسعه يافته است. اين روش تعميمي از روش هاي تندترين شيب و برزيليا-بوروين است.در اين پايان نامه همگرايي R-خطي اين روش اثبات مي شود و همچنين برخي از روش هاي گراديان دوري مورد مطالعه قرار مي گيرد.بررسي طول گام يوان و خواص طيفي روش هاي گراديان از ديگراهداف اين پايان نامه مي باشد.

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.

   {\\textbf{{چكيده}}} \\\\{\\\\ابتدا، براساس مقاله‌ي\\cite{C2}معادلات ديفرانسيل-انتگرال كسري($FDIEs $) را روي يك كلاس از مشتقات توسعه‌يافته($-B $عملگر) تعريف مي‌كنيم سپس آن را معادلات ديفرانسيل-انتگرال كسري توسعه‌يافته($GFDIEs $) نامگذاري مي‌كنيم. روش هم‌مكاني رابراي فرم‌هاي خطي و غير خطي ها گسترش مي‌دهيم. تقريب‌هاي عددي از ايده روش‌هاي هم‌مكانيبراي حل معادلات انتگرال استفاده مي‌كند. از چندجمله‌اي‌هاي لژاندر به منظور تقريبجواب‌هاي در فضاي با بعد متناهي به همراه همگرايي استفاده مي‌شود. برخي از مثال‌هايكه در آن هسته‌ي$ -B $ عملگرها را تغيير مي‌دهيم در انجامتحقيقات عددي در نظر گرفته مي‌شود. در قسمت دوم، براساس مقاله‌ي\\cite{C3}به معرفي يك روش عددي با مرتبه‌ دقت بالا برايحل معادله‌ي كاتانو با مشتق كسري زماني كه اساس روش طيفي گالركين-لژاندر در بعدمكان و روش هم‌مكاني چپيشف در بعد زمان است، مي پردازيم. در اين روش جواب تقريبيبه جواب واقعي مسأله همگراست و از مرتبه $O(N^{-m}M^{\\sigma} +N^{-m}+M^{\\sigma}) $ مي‌باشدكه در آن $ m \\geq 1 $ و $\\sigma > 1 $ . همچنين، به ترتيب $ N $ و $M $ تعداد گره‌ها در بعد مكان و زمان است. خطايبهينه‌ي كراندار قبلي از روش نيمه گسسته و پايدار و همگرايي طرح تمام گسسته   به‌طور كامل مورد بحث قرار مي‌گيرد. نتايج عدديكارايي اين روش را در بعد زمان و مكان تاييد مي‌كند.

In this thesis, we give a novel one parameter algebraic functional equation for fractional resolvent families. 

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.

In this thesis, we give a new distribution of a new >- F(HCF) distribution. Since the Burr distribution of the most special case of this family is theHyperbolic Cosine New Burr distribution. We also discuss simulation method , also maximumlikelihood minimum spaccing estimators of the parameters of the distribution . The new distributioncan be use effectively in the analysis of survival data .Show that the distribution of (HCB)Compared to distributions New Burr (NB), Weibull distribution (W), Log normal(LN) is flexibieto fit the data.  

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.   

  ‎‎‎In multiobjective optimization, several different objective should be optimized which are in conflict in general. Thus, the objective space is a set of vectors. For comparing these vectors a partial order is needed. Almost in all cases, this order is defined by a cone. This thesis studies multiobjective problems in which the related cone is a polyhedral cone. For polyhedral cones, it is shown how to find vectors in the positive dual cone that are needed for a scalarized objective function. Instructive examples are presented. In this thesis, by using a special kind of polyhedral cone namely, dilating cones and applying nonlinear scalarization proper are characterized. A similar characterization is derived for weakly efficient solution, for which no convexity hypotheses are required. Finally, when the feasible set is given by a cone constraint, some necessary and sufficient optimality conditions via a kind of scalar nonlinear Lagrangian are obtained.

  Adaptive web sampling design is a flexible >In these designs, an initial sample is first taken, then the selection of the next units is based on thecompound distribution: that is, with a predetermined probability, the units are selected through thelinks that are connected to the previous sample, or a unit is selected randomly. In this thesis, this

  ‎The ‎objective ‎of ‎this ‎thesis ‎is ‎to ‎obtain ‎sufficient ‎condition‎s for the dynamics of a vector field on the two dimensional center manifold to be topologically equivalent with the versal deformation of two dimensional Bognanov-Takens bifurcation. Next, using the results of this part, the bursting behaviours and the related bifurcations of the neurons in the Pre-Botzinger Complex is investigated.

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.

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.

  Initial value problems and Boundary value problems have important applications in various branches of pure and applied sciences, including astrophysics, structural engineering, optimization, and economics. In some particular situations it is possible to find a general solution of the equation, but in general it is not possible. In most cases, only approximate solutions can be expected. Accordingly, a large number of methods for the numerical solution of IVPs and BVPs have been proposed in literature. In this thesis, firstly, based on Bernoulli polynomials and using spectral methods, an efficient numerical method is proposed to approximate the analytic solution of an initial value problem. Then, using the Birkhoff- Lagrange-collocation method, a numerical algorithm for solving boundary value problems are studied. Finally, the numerical expriements show that the new methods is efficient.

  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.