@article { author = {Sayyari, Yamin}, title = {New Bounds for Entropy of Information Sources}, journal = {Wavelet and Linear Algebra}, volume = {7}, number = {2}, pages = {1-9}, year = {2020}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {10.22072/wala.2020.111881.1240}, abstract = {Shannon's entropy plays an important role in information theory, dynamical systems and thermodynamics. In this paper we applying Jensen's inequality in information theory and we obtain some results for the Shannon's entropy of random variables and Shannon's entropy of stochastic process. Also we obtain upper bound and lower bound for Shannon's entropy of information sources.}, keywords = {Entropy,Shannon's entropy,Information source,convex function,random variable}, title_fa = {کران های جدید برای آنتروپی منبع های اطلاعات}, abstract_fa = {آنتروپی شانون نقش مهمی را در نظریه اطلاعات، سیستم های دینامیکی و ترمودینامیک دارد. ما در این مقاله با استفاده از نامساوی ینسن برخی نتایج را برای آنتروپی شانون متغیرهای تصادفی و آنتروپی شانون فرایندهای تصادفی بدست آورده ایم. همچنین یک کران بالا و یک کران پایین برای آنتروپی شانون منبع های اطلاعات بدست آورده ایم.}, keywords_fa = {آنتروپی,آنتروپی شانون,منبع اطلاعات,تابع محدب,متغیر تصادفی}, url = {https://wala.vru.ac.ir/article_46669.html}, eprint = {https://wala.vru.ac.ir/article_46669_8c805aad6947b42252be16405f2e6554.pdf} } @article { author = {Barsam, Hasan}, title = {Some New Hermite-Hadamard Type Inequalities for Convex Functions}, journal = {Wavelet and Linear Algebra}, volume = {7}, number = {2}, pages = {11-22}, year = {2020}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {10.22072/wala.2020.117932.1260}, abstract = {Convex sets and convex functions play a fundamental role in the development of various fields of pure and applied mathematics.  Recently, many new generalizations of inequalities with respect to Hermite-Hadamard  have been proposed in the literature. In this paper,  some  new  inequalities of the Hermite-Hadamard type for differentiable convex functions are given. These new inequalities are based on the second derivative functions.}, keywords = {Hermite-Hadamard's inequality,functional inequality,convex function,H"older's inequality,power-mean inequality}, title_fa = {برخی نامساوی های جدید از نوع نامساوی هرمیت-هادامارد برای توابع محدب}, abstract_fa = {مجموعه های محدب و توابع محدب نقشی اساسی در توسعه رشته های مختلف ریاضی کاربردی و محض دارد.اخیرأ تعمیم های مختلفی برای نامساوی هرمیت-هادامارد پیشنهاد شده است. در این مقاله برخی نتایج جدید از نامساوی هرمیت-هادامارد برای توابع محدب ارائه نموده ایم این نامساوی ها بر حسب مشتق دوم توابع می باشند.}, keywords_fa = {نامساوی هرمیت-هادامارد,نامساوی تابعی,نامساوی هولدر}, url = {https://wala.vru.ac.ir/article_46671.html}, eprint = {https://wala.vru.ac.ir/article_46671_775fcdb65026bb808244fc5f86153d37.pdf} } @article { author = {Barootkoob, S.}, title = {The Banach algebras with generalized matrix representation}, journal = {Wavelet and Linear Algebra}, volume = {7}, number = {2}, pages = {23-29}, year = {2020}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {10.22072/wala.2020.122402.1273}, abstract = {A Banach algebra $\mathfrak{A}$ has a generalized Matrix representation if there exist the algebras $A, B$, $(A,B)$-module $M$ and $(B,A)$-module $N$ such that $\mathfrak{A}$ is isomorphic to the generalized matrix Banach algebra $\Big[\begin{array}{cc}A & \ M \\N & \ B%\end{array}%\Big]$.In this paper, the algebras with generalized matrix representation will be characterized. Then we show that there is a unital permanently weakly amenable  Banach algebra $A$ without generalized matrix representation such that $H^1(A,A)=\{0\}$.This implies that there is a unital Banach algebra $A$ without any triangular matrix representation such that $H^1(A,A)=\{0\}$  and gives a negative answer to the open question of \cite{D}.}, keywords = {Banach algebra,idempotent,generalized matrix Banach algebra}, title_fa = {جبرهای باناخ دارای نمایش ماتریسی تعمیم یافته}, abstract_fa = {گوییم یک جبر باناخ $\mathfrak{A}$ دارای نمایش ماتریسی تعمیم یافته است هرگاه جبرهای باناخ A‎, ‎B‎ و (A,B)-مدول M و (B,A)-مدول N موجود باشند به طوری که $\mathfrak{A}$ با جبر باناخ ماتریسی تعمیم یافته $\Big[\begin{array}{cc}‎ ‎A & \ M \\‎ ‎N & \ B%‎ ‎\end{array}%‎ ‎\Big]$ یکریخت باشد. در این مقاله، جبرهای باناخی را که دارای نمایش ماتریسی تعمیم یافته اند را مشخص می کنیم. سپس نشان می دهیم که یک جبر باناخ دائما میانگین پذیر ضعیف یکدار A موجود است که دارای نمایش ماتریسی تعمیم یافته نیست و $H^1(A,A)=\{0\}$‎. بویژه یک جبر باناخ یکدار A موجود است که دارای نمایش ماتریسی مثلثی نیست و $H^1(A,A)=\{0\}$، که این یک پاسخ منفی به سوال پاسخ باز \cite{D}‎ می دهد.}, keywords_fa = {جبرباناخ,عنصر خودتوان,جبر باناخ ماتریسی تعمیم یافته}, url = {https://wala.vru.ac.ir/article_46689.html}, eprint = {https://wala.vru.ac.ir/article_46689_9bbcbc7bf6da8a6523c12efd91f48d91.pdf} } @article { author = {Khoddami, Ali Reza}, title = {Weak and cyclic amenability of certain function algebras}, journal = {Wavelet and Linear Algebra}, volume = {7}, number = {2}, pages = {31-41}, year = {2020}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {10.22072/wala.2020.124774.1280}, abstract = {We consider $C^{b\varphi}(K)$ to be the space $C^b(K)$ equipped with the product $f\cdot g=f\varphi g$ for all $f, g\in C^b(K)$ where, $K=\overline{B_1^{(0)}}$ is the closed unit ball of a non-zero normed vector space $A$ and $\varphi$ is a non-zero element of $A^*$ such that $\Vert \varphi \Vert\leq 1$. We define $\Vert f \Vert_\varphi=\Vert f\varphi \Vert_\infty$ for all $f\in C^{b\varphi}(K)$. Some relations between the dual spaces of $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)$ are investigated. Also we characterize the derivations from $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)$ into $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)^*$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)^*$ respectively. Finally we investigate the weak and cyclic amenability of $(C^{b\varphi}(K), \Vert \cdot \Vert_\infty)$ and $(C^{b\varphi}(K), \Vert \cdot \Vert_\varphi)$.}, keywords = {Completely regular,derivation,inner derivation,Weak amenability,cyclic amenability}, title_fa = {میانگین پذیری ضعیف و دوری جبرهای تابعی خاص}, abstract_fa = {}, keywords_fa = {}, url = {https://wala.vru.ac.ir/article_46730.html}, eprint = {https://wala.vru.ac.ir/article_46730_cb5d16417380487748f14b2d53836fdc.pdf} } @article { author = {Ebrahimi Meymand, Ali}, title = {The structure of the set of all $C^*$-convex maps in $*$-rings}, journal = {Wavelet and Linear Algebra}, volume = {7}, number = {2}, pages = {43-51}, year = {2020}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {10.22072/wala.2020.125309.1282}, abstract = {In this paper, for every unital $*$-ring $\mathcal{S}$, we investigate the Jensen's inequality preserving maps on $C^*$-convex subsets of $\mathcal{S}$, which we call them $C^*$-convex maps on $\mathcal{S}$. We consider an involution for maps on $*$-rings, and we show that for every $C^*$-convex map $f$ on the $C^*$-convex set $B$ in $\mathcal{S}$, $f^*$ is also a $C^*$-convex map on $B$. We prove that  in the unital commutative $*$-rings, the set of all $C^*$-convex maps ($C^*$-affine maps) on a $C^*$-convex set $B$, is also a $C^*$-convex set. In addition, we prove some results for increasing $C^*$-convex maps. Moreover, it is proved that the set of all $C^*$-affine maps on $B$, is a $C^*$-face of the set of all $C^*$-convex maps on $B$ in the unital commutative $*$-rings. Finally, some examples of $C^*$-convex maps and $C^*$-affine maps in $*$-rings are given.}, keywords = {$C^*$-affine map,$C^*$-convex map,$C^*$-face,$*$-ring}, title_fa = {The structure of the set of all C*-convex maps in *-rings}, abstract_fa = {}, keywords_fa = {}, url = {https://wala.vru.ac.ir/article_46731.html}, eprint = {https://wala.vru.ac.ir/article_46731_27950884887f822551d8a043e7881345.pdf} }