The Stochastic Leibniz Formula for Volterra Integrals under Enlarged Filtrations

2018 ◽  
Author(s):  
Markus Hess
Keyword(s):  
Leibniz Formula

"Efficiency Comparison of Algorithms for Finding Determinants Via Permutations "

2021 ◽  
Vol 8 (1) ◽  
pp. 56-65
Author(s):  
Lugen M. Zake Sheet
Keyword(s):  
Linear Algebra ◽  
Comparison Of Algorithms ◽  
Leibniz Formula ◽  
Laplace Expansion ◽  
Quadratic Matrix ◽  
Efficiency Comparison ◽  
Selection Of

"Determiners have been used extensively in a selection of applications throughout history. It also biased many areas of mathematics such as linear algebra. There are algorithms commonly used for computing a matrix determinant such as: Laplace expansion, LDU decomposition, Cofactor algorithm, and permutation algorithms. The determinants of a quadratic matrix can be found using a diversity of these methods, including the well-known methods of the Leibniz formula and the Laplace expansion and permutation algorithms that computes the determinant of any n×n matrix in O(n!). In this paper, we first discuss three algorithms for finding determinants using permutations. Then we make out the algorithms in pseudo code and finally, we analyze the complexity and nature of the algorithms and compare them with each other. We present permutations algorithms and then analyze and compare them in terms of runtime, acceleration and competence, as the presented algorithms presented different results.

The Generalized Leibniz Formula

1950 ◽  
Vol 57 (7P1) ◽  
pp. 459-466
Author(s):  
C. J. Coe
Keyword(s):  
Leibniz Formula

scholarly journals The Discrete Analog of the Newton-Leibniz Formula in the Problem of Summation over Simplex Lattice Points

2019 ◽  
pp. 503-508
Author(s):  
Evgeniy K. Leinartas ◽  
Olga A. Shishkina
Keyword(s):  
Discrete Analog ◽  
Lattice Points ◽  
Primitive Function ◽  
Leibniz Formula ◽  
Simplex Lattice ◽  
Definition Of

Definition of the discrete primitive function is introduced in the problem of summation over simplex lattice points. The discrete analog of the Newton-Leibniz formula is found

La metafísica modal de Leibniz: su fundamentación de la contingencia hacia 1686 y su concepción integral de madurez

2016 ◽  
Vol 59 (73) ◽  
pp. 47
Author(s):  
Maximiliano Escobar Viré
Keyword(s):  
Leibniz Formula

<p class='p1'>Si Dios es la razón suficiente del mundo, entonces parece seguirse que todos los eventos son consecuencia necesaria de un ser necesario. Para evadir esta conclusión, Leibniz formula en la década de 1670 una concepción modal que funda la contingencia en un rasgo lógico eintrínseco de las ideas de las cosas: la posibilidad de concebir la idea contraria sin contradicción. Hacia 1686, Leibniz complementa esta primera concepción con lo que considera su solución definitiva al problema de la contingencia: la teoría del análisis infinito. Sin embargo, en otros escritos de ese año, propone dos vías alternativas de fundamentación de la contingencia. Este trabajo sugiere que esa pluralidad de modelos explicativos converge en una concepción integral de las modalidades que subyace como trasfondo de la reflexión modal leibniziana. </p>

Gewöhnliche lineare Differentialgleichungen n−ter Ordnung mit Distributionskoeffizienten

1980 ◽  
Vol 85 (3-4) ◽  
pp. 291-298 ◽  
Author(s):  
Rainer Pfaff
Keyword(s):  
Differential Equations ◽  
Continuous Solution ◽  
Initial Conditions ◽  
Linear Differential Equations ◽  
First Order ◽  
Integrable Functions ◽  
Leibniz Formula ◽  
Linear Differential ◽  
Ordinary Linear Differential Equations ◽  
Derivatives Of

SynopsisWe give a formula (4) for a variety of ordinary linear differential equations of order n with distributional coefficients. There appear as coefficients distributions of order k ≦ n/2, i.e. these distributions are kth distributional derivatives of locally L-integrable functions. With a suitable transformation (7) the differential equations can be transformed into first order systems (8) with integrable coefficients. From this follows the existence of a continuous solution, which can be uniquely determined by proper initial conditions.The coefficients in the differential equations considered are chosen as general as possible but such that a transformation into a system with integrable coefficients can be performed, and that all products are defined by Leibniz' formula.

The Generalized Leibniz Formula

1950 ◽  
Vol 57 (7) ◽  
pp. 459
Author(s):  
C. J. Coe
Keyword(s):  
Leibniz Formula

scholarly journals Pinning Synchronization for Complex Networks with Interval Coupling Delay by Variable Subintervals Method and Finsler’s Lemma

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Dawei Gong ◽  
Frank L. Lewis ◽  
Liping Wang ◽  
Dong Dai ◽  
Shuang Zhang
Keyword(s):  
Linear Matrix Inequality ◽  
Complex Networks ◽  
Pinning Control ◽  
Stability Theorem ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Coupling Delay ◽  
Leibniz Formula ◽  
The Stability ◽  
Finsler’S Lemma

The pinning synchronous problem for complex networks with interval delays is studied in this paper. First, by using an inequality which is introduced from Newton-Leibniz formula, a new synchronization criterion is derived. Second, combining Finsler’s Lemma with homogenous matrix, convergent linear matrix inequality (LMI) relaxations for synchronization analysis are proposed with matrix-valued coefficients. Third, a new variable subintervals method is applied to expand the obtained results. Different from previous results, the interval delays are divided into some subdelays, which can introduce more free weighting matrices. Fourth, the results are shown as LMI, which can be easily analyzed or tested. Finally, the stability of the networks is proved via Lyapunov’s stability theorem, and the simulation of the trajectory claims the practicality of the proposed pinning control.

scholarly journals Formalizing Calculus without Limit Theory in Coq

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1377
Author(s):  
Yaoshun Fu ◽  
Wensheng Yu
Keyword(s):  
Mathematical Theory ◽  
Control Function ◽  
Taylor Formula ◽  
Difference Quotient ◽  
Fundamental Theory ◽  
Limit Theory ◽  
Leibniz Formula ◽  
New Form ◽  
The Difference ◽  
Definition Of

Formal verification of mathematical theory has received widespread concern and grown rapidly. The formalization of the fundamental theory will contribute to the development of large projects. In this paper, we present the formalization in Coq of calculus without limit theory. The theory aims to found a new form of calculus more easily but rigorously. This theory as an innovation differs from traditional calculus but is equivalent and more comprehensible. First, the definition of the difference-quotient control function is given intuitively from the physical facts. Further, conditions are added to it to get the derivative, and define the integral by the axiomatization. Then some important conclusions in calculus such as the Newton–Leibniz formula and the Taylor formula can be formally verified. This shows that this theory can be independent of limit theory, and any proof does not involve real number completeness. This work can help learners to study calculus and lay the foundation for many applications.

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