Institute of Mathematics AS CR, v. v. i.
Not a member yet
44818 research outputs found
Sort by
Properties on subclass of Sakaguchi type functions using a Mittag-Leffler type Poisson distribution series
Get PDFsummary:Few subclasses of Sakaguchi type functions are introduced in this article, based on the notion of Mittag-Leffler type Poisson distribution series. The class is defined, and the necessary and sufficient condition, convex combination, growth distortion bounds, and partial sums are discussed
Generalized derivations with power values on rings and Banach algebras
Get PDFsummary:Let be a prime ring and a nonzero ideal of The purpose of this paper is to classify generalized derivations of satisfying some algebraic identities with power values on More precisely, we consider two generalized derivations and of satisfying one of the following identities: \begin {itemize} \item [(1)] for all \item [(2)] for all \end {itemize} for two fixed positive integers , and an element of the extended centroid of . Finally, as an application, the same identities are studied locally on nonvoid open subsets of a prime Banach algebra
Dual modules and reflexive modules with respect to a semidualizing module
No full textsummary:Let be a semidualizing module over a commutative ring. We first investigate the properties of -dual, -torsionless and -reflexive modules. Then we characterize some rings such as coherent rings, -coherent rings and FP-injectivity of using -dual, -torsionless and -reflexive properties of some special modules
Characterizations of incidence modules
No full textsummary:Let be an associative ring and be a left -module. We introduce the concept of the incidence module of a locally finite partially ordered set over . We study the properties of and give the necessary and sufficient conditions for the incidence module to be an IN-module, \EIN -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of \EIN -modules is closed under direct product and upper triangular matrix modules
Linear congruences and a conjecture of Bibak
No full textsummary:We address three questions posed by K. Bibak (2020), and generalize some results of K. Bibak, D. N. Lehmer and K. G. Ramanathan on solutions of linear congruences . In particular, we obtain explicit expressions for the number of solutions, where 's are squares modulo . In addition, we obtain expressions for the number of solutions with order restrictions or with strict order restrictions in some special cases. In these results, the expressions for the number of solutions involve Ramanujan sums and are obtained using their properties
DDIMCache: An enhanced text-to-image diffusion model on mobile devices
Get PDFsummary:On June 11, 2024, OpenAI announced a collaboration with Apple to deeply integrate the ChatGPT generative language model into Apple's product lineup. With support from various generative AI models, devices like smartphones will become more intelligent. The text-to-image diffusion model, known for its stable and superior generative capabilities, has gained wide recognition in image generation and will undoubtedly play a crucial role on mobile devices. However, the large size and complex architecture of diffusion models result in high computational costs and slower execution speeds. As a result, diffusion models require high-end GPUs or cloud-based inference, which often raises personal privacy and data security. This paper presents a multiplicative effect joint optimization method for complex models such as diffusion models, enabling efficient execution on mobile devices. The method integrates multiple optimization strategies, leveraging their interactions to create synergies and enhance overall performance. Building on this multiplicative effect joint optimization approach, we have introduced DDIMCache, an enhanced text-to-image diffusion model. DDIMCache maintains image generation quality while achieving optimal speed, generating 512-512 images in approximately 6 seconds. This provides powerful image generation capabilities and an enhanced user experience for mobile users.In addition, as a foundation model, Stable Diffusion supports more applications such as image editing, inpainting, style transfer, and super-resolution, all of which can have a significant impact. The ability to run the model entirely on mobile devices without an internet connection will open up endless possibilities