相关论文: Perpendicular Indiscernible Sequences in Real Clos…
We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.
We use the notion of collapse of generalized indiscernible sequences to classify various model theoretic dividing lines. In particular, we use collapse of n-multi-order indiscernibles to characterize op-dimension n; collapse of…
In the setting of nonstandard analysis we introduce the notion of flexible sequence. The terms of flexible sequences are external numbers. These are a sort of analogue for the classical \emph{O$ (\cdot ) $} and \emph{o$ (\cdot ) $} notation…
Previously, in an effective field theory formulated by us, we have carried out parameter-free calculations of a large number of low-energy two-nucleon properties. An experiment at the Institut Laue-Langevin is currently measuring…
We extend the theory of d-separation to cases in which data instances are not independent and identically distributed. We show that applying the rules of d-separation directly to the structure of probabilistic models of relational data…
Given a family of world-sheet superconformal field theories related by marginal deformation, we can formulate superstring field theory based on any of these world-sheet theories. Background independence is the statement that these different…
The modern definition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article,…
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for…
In this manuscript, new algebraic and analytic aspects of the orthogonal polynomials satisfying $R_{II}$ type recurrence relation given by \begin{align*} \mathcal{P}_{n+1}(x) = (x-c_n)\mathcal{P}_n(x)-\lambda_n…
We give a full solution to the question of existence of indiscernibles in dependent theories by proving the following theorem: for every $\theta$ there is a dependent theory $T$ of size $\theta$ such that for all $\kappa$ and $\delta$,…
The correlation between a random sequence and its transformed sequences is studied. In the case of a permutation operation or, in other word, the shuffling operation, it is shown that the correlation can be so small that the sequences can…
Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have nice mathematical structures and good randomness properties…
This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over $C((x))$ and $\mathbb P^1_C\smallsetminus\{0,\infty\}$, where $C$ is…
In this paper we study some basic properties of rough $I$-convergent double sequences in the line of D$\ddot{u}$ndar [8]. We also study the set of all rough $I$-limits of a double sequence and relation between boundedness and rough…
This paper presents a simulation-based framework for sequential inference from partially and discretely observed point process (PP's) models with static parameters. Taking on a Bayesian perspective for the static parameters, we build upon…
We introduce the new concept of joint nonlinear complexity for multisequences over finite fields and we analyze the joint nonlinear complexity of two families of explicit inversive multisequences. We also establish a probabilistic result on…
This thesis is divided into three parts. In the first part, we give an introduction to J. Harrison's theory of differential chains. In the second part, we apply these tools to generalize the Cauchy theorems in complex analysis. Instead of…