相关论文: SPM Bulletin 11

The two of us have shared a fascination with James Victor Uspensky's 1937 textbook $Introduction \, to \, Mathematical \, Probability$ ever since our graduate student days: it contains many interesting results not found in other books on…

The first chapter serves as an introduction to the MSSM. I briefly review the model and explain why stops and sbottoms provide an interesting playground for exploring and testing this model. In the second chapter I discuss stop and sbottom…

Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type…

The wealth of experimental data collected at laboratory experiments suggests that there is some scale separation between the Standard Model (SM) and phenomena beyond the SM (BSM). New phenomena can manifest itself as small corrections to SM…

A series of recent papers by Bergfalk, Lupini and Panagiotopoulus developed the foundations of a field known as `definable algebraic topology,' in which classical cohomological invariants are enriched by viewing them as groups with a Polish…

This $2^{nd}$-edition article is intended to be an up-to-date archive of the current state of the questions: Which finitely generated groups $G$: have semistable fundamental group at infinity; are simply connected at infinity; are such that…

This paper presents three new families of fractional Sobolev spaces and their accompanying theory in one-dimension. The new construction and theory are based on a newly developed notion of weak fractional derivatives, which are natural…

Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…

These notes are based on a series of lectures given first at the University of Warwick in spring 2008 and then at the Courant Institute, Imperial College London, and EPFL. It is an attempt to give a reasonably self-contained presentation of…

This thesis opens with an introductory discussion, where the reader is gently led to the world of topological combinatorics, and, where the results of this Habilitationsschrift are portrayed against the backdrop of the broader philosophy of…

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…

We generalize the notion of Monk's schema in such a way to integrate finite dimensions. This allows us to lift a plathora of deep results proved for finite dimensions to the infinite dimensional case, like the solution to problem 2.12 in…

In the year 2014, the field of selection principles found its way into several additional, fascinating mathematical realms. The field enters the consensus as a mainstream part of set theory and topology, and as a promising direction for…

This paper presents a rigorous theoretical extension of the Smagorinsky model for turbulence simulations. The author builds on its fundamental framework, addressing known limitations, and making new mathematical advances. Specifically, this…

This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…

This is the Snowmass2021 Energy Frontier (EF) Beyond the Standard Model (BSM) report. It combines the EF topical group reports of EF08 (Model-specific explorations), EF09 (More general explorations), and EF10 (Dark Matter at Colliders). The…

This note is written for a book dedicated to outstanding St-Petersburg mathematicians and timed to the ICM-2022 in St-Petersburg. In accordance with the plan of ICM-organizers, we try to tell about one of the most prominent Rokhlin's…

Addendum to the paper Combinatorics of the Modular Group II The Kontsevich integrals, hep-th/9201001, by C. Itzykson and J.-B. Zuber (3 pages)

Computational astrophysics has undergone unprecedented development over the last decade, becoming a field of its own. The challenge ahead of us will involve increasingly complex multi-scale simulations. These will bridge the gap between…

This special issue is dedicated to starshades: science, engineering, technology and programmatics. Our reasons for organizing this special issue are several fold. First as a new technology and with research accomplished in many…