scholarly journals LOOK, KNAVE

Author(s):  
THOMAS MORRILL

Abstract We examine a recursive sequence in which $s_n$ is a literal description of what the binary expansion of the previous term $s_{n-1}$ is not. By adapting a technique of Conway, we determine the limiting behaviour of $\{s_n\}$ and dynamics of a related self-map of $2^{\mathbb {N}}$ . Our main result is the existence and uniqueness of a pair of binary sequences, each the complement-description of the other. We also take every opportunity to make puns.

2021 ◽  
Vol 5 (2) ◽  
pp. 32
Author(s):  
Esmehan Uçar ◽  
Sümeyra Uçar ◽  
Fırat Evirgen ◽  
Necati Özdemir

It is possible to produce mobile phone worms, which are computer viruses with the ability to command the running of cell phones by taking advantage of their flaws, to be transmitted from one device to the other with increasing numbers. In our day, one of the services to gain currency for circulating these malignant worms is SMS. The distinctions of computers from mobile devices render the existing propagation models of computer worms unable to start operating instantaneously in the mobile network, and this is particularly valid for the SMS framework. The susceptible–affected–infectious–suspended–recovered model with a classical derivative (abbreviated as SAIDR) was coined by Xiao et al., (2017) in order to correctly estimate the spread of worms by means of SMS. This study is the first to implement an Atangana–Baleanu (AB) derivative in association with the fractional SAIDR model, depending upon the SAIDR model. The existence and uniqueness of the drinking model solutions together with the stability analysis are shown through the Banach fixed point theorem. The special solution of the model is investigated using the Laplace transformation and then we present a set of numeric graphics by varying the fractional-order θ with the intention of showing the effectiveness of the fractional derivative.


2011 ◽  
Vol 374-377 ◽  
pp. 2605-2609
Author(s):  
Lei Shi ◽  
Li Gao

Logit model is among the most important model in SUE DTA study. A lot of work have been done based on Logit model. As the other very important SUE DTA model, Probit model has not been the focus of many researcher. This paper presents a SUE model based on Probit model, which aims at building up the Probit model with constant demand. The existence and uniqueness of the model is presented, Finally, a algorithm is given.


1990 ◽  
Vol 1 (1) ◽  
pp. 91-100 ◽  
Author(s):  
Dominique Blanchard ◽  
Hamid Ghidouche

This paper is concerned with the mathematical study of a nonlinear system modelling an irreversible phase change problem. Uniqueness of the solution is proved using the accretivity of the system in (L1)2. Expressing one of the two unknowns as an explicit functional of the other reduces the system to a single nonlinear evolution equation and ultimately leads to an existence theorem.In this paper the existence and uniqueness of the solution of a nonlinear system modelling some irreversible phase changes is established.


2020 ◽  
Vol 23 (07) ◽  
pp. 2050043
Author(s):  
MAXIM BICHUCH ◽  
KE CHEN

In a crisis, when faced with insolvency, banks can sell stock in a dilutive offering in the stock market and borrow money in order to raise funds. We propose a simple model to find the maximum amount of new funds the banks can raise in these ways. To do this, we incorporate market confidence of the bank together with market confidence of all the other banks in the system into the overnight borrowing rate. Additionally, for a given cash shortfall, we find the optimal mix of borrowing and stock selling strategy. We show the existence and uniqueness of Nash equilibrium point for all these problems. Finally, using this model we investigate if banks have become safer since the crisis. We calibrate this model with market data and conduct an empirical study to assess safety of the financial system before, during after the last financial crisis.


2019 ◽  
Vol 29 (1) ◽  
pp. 137-152 ◽  
Author(s):  
Ross G. Pinsky

AbstractFor $$\tau \in {S_3}$$, let $$\mu _n^\tau $$ denote the uniformly random probability measure on the set of $$\tau $$-avoiding permutations in $${S_n}$$. Let $${\mathbb {N}^*} = {\mathbb {N}} \cup \{ \infty \} $$ with an appropriate metric and denote by $$S({\mathbb{N}},{\mathbb{N}^*})$$ the compact metric space consisting of functions $$\sigma {\rm{ = }}\{ {\sigma _i}\} _{i = 1}^\infty {\rm{ }}$$ from $$\mathbb {N}$$ to $${\mathbb {N}^ * }$$ which are injections when restricted to $${\sigma ^{ - 1}}(\mathbb {N})$$; that is, if $${\sigma _i}{\rm{ = }}{\sigma _j}$$, $$i \ne j$$, then $${\sigma _i} = \infty $$. Extending permutations $$\sigma \in {S_n}$$ by defining $${\sigma _j} = j$$, for $$j \gt n$$, we have $${S_n} \subset S({\mathbb{N}},{{\mathbb{N}}^*})$$. For each $$\tau \in {S_3}$$, we study the limiting behaviour of the measures $$\{ \mu _n^\tau \} _{n = 1}^\infty $$ on $$S({\mathbb{N}},{\mathbb{N}^*})$$. We obtain partial results for the permutation $$\tau = 321$$ and complete results for the other five permutations $$\tau \in {S_3}$$.


2000 ◽  
Vol 10 (08) ◽  
pp. 1263-1276
Author(s):  
DANIELE ANDREUCCI ◽  
ANTONIO FASANO ◽  
RICCARDO RICCI

We prove the existence and uniqueness of solutions, for small times, for a mathematical scheme modeling the Ziegler–Natta process of polymerization. The model consists, essentially, of two diffusion problems at two different space scales, one relative to the microscopical catalyst pellets, the other to the macroscopical aggregate of those pellets. The coupling between the two scales is of nonstandard nature.


2003 ◽  
Vol 13 (06) ◽  
pp. 875-892 ◽  
Author(s):  
Jacek Banasiak

The paper deals with an analysis of well-posedness of the Boltzmann-like semiconductor equation with unbounded collision frequency, introduced recently by Majorana and Milazzo.17The equation is derived by writing the balance of the electrons lost and gained at each energy level due to scattering on the crystalline lattice of the semiconductor. As the total amount of electrons is expected to be constant, the process can be viewed as a Markov process, and from the functional analytic point of view it fits into the general theory of substochastic semigroups.5,26In this paper we present two methods of solving the evolution equation describing this process: one is a generalization of the approach of Reuter and Ledermann23to solving differential equations governing Markov processes with denumerably many states, while the other is based on the Kato–Voigt perturbation technique for substochastic semigroups.15,26,2,3,5The combination of these two techniques is a powerful tool yielding strong results on the existence and uniqueness of conservative solutions. It is also shown how the solution method employed in Ref. 17 fits into the theory developed in this paper.


2021 ◽  
Author(s):  
Vincent Conitzer ◽  
Christian Kroer ◽  
Eric Sodomka ◽  
Nicolas E. Stier-Moses

Budgets play a significant role in ad markets that implement sequential auctions such as those hosted by internet companies. In “Multiplicative Pacing Equilibria in Auction Markets,” the authors look at pacing in an ad marketplace using the lens of game theory. The goal is understanding how bids must be shaded to maximize advertiser welfare, at equilibrium. Motivated by the real-world auction mechanism, they construct a game where advertisers in the auctions choose a multiplicative factor not larger than 1 to possibly reduce their bids and best respond to the other advertisers. The article studies the theoretical properties of the game such as existence and uniqueness of equilibria, offers an exact algorithm to compute them, connects the game to well-known abstractions such as Fisher markets, and performs a computational study with real-world-inspired instances. The main insights are that the solutions to the studied game can be used to improve the outcomes achieved by a closer-to-reality dynamic pacing algorithm and that buyers do not have an incentive to misreport bids or budgets when there are enough participants in the auction.


Author(s):  
Niels Ole Finnemann

Electronic text can be defined on two different, though interconnected, levels. On the one hand, electronic text can be defined by taking the notion of “text” or “printed text” as the point of departure. On the other hand, electronic text can be defined by taking the digital format as the point of departure, where everything is represented in the binary alphabet. While the notion of text in most cases lends itself to being independent of medium and embodiment, it is also often tacitly assumed that it is in fact modeled on the print medium, instead of, for instance, on hand-written text or speech. In late 20th century, the notion of “text” was subjected to increasing criticism, as can be seen in the question that has been raised in literary text theory about whether “there is a text in this class.” At the same time, the notion was expanded by including extralinguistic sign modalities (images, videos). A basic question, therefore, is whether electronic text should be included in the enlarged notion that text is a new digital sign modality added to the repertoire of modalities or whether it should be included as a sign modality that is both an independent modality and a container that can hold other modalities. In the first case, the notion of electronic text would be paradigmatically formed around the e-book, which was conceived as a digital copy of a printed book but is now a deliberately closed work. Even closed works in digital form will need some sort of interface and hypertextual navigation that together constitute a particular kind of paratext needed for accessing any sort of digital material. In the second case, the electronic text is defined by the representation of content and (some parts of the) processing rules as binary sequences manifested in the binary alphabet. This wider notion would include, for instance, all sorts of scanning results, whether of the outer cosmos or the interior of our bodies and of digital traces of other processes in-between (machine readings included). Since other alphabets, such as the genetic alphabet and all sorts of images may also be represented in the binary alphabet, such materials will also belong to the textual universe within this definition. A more intriguing implication is that born-digital materials may also include scripts and interactive features as intrinsic parts of the text. The two notions define the text on different levels: one is centered on the Latin, the other on the binary alphabet, and both definitions include hypertext, interactivity, and multimodality as constituent parameters. In the first case, hypertext is included as a navigational, paratextual device; whereas in the second case, hypertext is also incorporated in the narrative within an otherwise closed work or as a constituent element on the textual universe of the web, where it serves the ongoing production of (possibly scripted) connections and disconnections between blocks of textual content. Since the early decades of early 21st century still represent only the very early stages of the globally distributed universe of web texts, this is also a history of the gradual unfolding of the dimensions of these three constituencies—hypertext, interactivity, and multimodality. The result is a still-expanding repertoire of genres, including some that are emerging via path dependency; some via remediation; and some as new genres that are unique for networked digital media, including “social media texts” and a growing variety of narrative and discursive multiple-source systems.


Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 968
Author(s):  
Artion Kashuri ◽  
Badreddine Meftah ◽  
Pshtiwan Othman Mohammed ◽  
Alina Alb Lupaş ◽  
Bahaaeldin Abdalla ◽  
...  

An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition and its properties. Furthermore, there is a strong correlation between convexity and symmetry concepts. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the last few years. In this study, by using a new identity, we establish some new fractional weighted Ostrowski-type inequalities for differentiable quasi-convex functions. Further, further results for functions with a bounded first derivative are given. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtain. The obtained results generalize and refine certain known results.


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