Results 171 to 180 of about 527,157 (233)
Relational Bundle Geometric Formulation of Non‐Relativistic Quantum Mechanics
Fortschritte der Physik, EarlyView.Abstract A bundle geometric formulation of non‐relativistic many‐particles Quantum Mechanics is presented. A wave function is seen to be a C$\mathbb {C}$‐valued cocyclic tensorial 0‐form on configuration space‐time seen as a principal bundle, while the Schrödinger equation flows from its covariant derivative, with the action functional supplying a ...
J. T. François, L. Ravera
wiley +1 more source
A Step‐by‐Step Workflow for Performing In Silico Clinical Trials With Nonlinear Mixed Effects Models
CPT: Pharmacometrics &Systems Pharmacology, EarlyView.ABSTRACT In silico clinical trials (ISCT) are computational frameworks that employ mathematical models to generate virtual patients and simulate their responses to new treatments, treatment regimens, or medical devices via simulations mirroring real‐world clinical trials.
Javiera Cortés‐Ríos +4 more
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Advanced Quantum Technologies, EarlyView.The hybrid approach to Quantum Supervised Machine Learning is compatible with Noisy Intermediate Scale Quantum (NISQ) devices but hardly useful. Pure quantum kernels requiring fault‐tolerant quantum computers are more promising. Examples are kernels computed by means of the Quantum Fourier Transform (QFT) and kernels defined via the calculation of ...
Massimiliano Incudini +2 more
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Entanglement Swapping for Partially Entangled Qudits and the Role of Quantum Complementarity
Advanced Quantum Technologies, EarlyView.The entanglement swapping protocol is extended to partially entangled qudit states and analyzed through complete complementarity relations. Analytical bounds on the average distributed entanglement are established, showing how the initial local predictability and entanglement constrain the operational distribution.
Diego S. Starke +3 more
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Algebra and Algebraic Number Theory [PDF]
, 1992 The 19th century was an age of deep qualitative transformations and, at the same time, of great discoveries in all areas of mathematics, including algebra. The transformation of algebra was fundamental in nature. Between the beginning and the end of the last century, or rather between the beginning of the last century and the twenties of this century ...
I. G. Bashmakova, A. N. Rudakov
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1982
In this chapter we shall introduce the concept of an algebraic number field and develop its basic properties. Our treatment will be classical, developing directly only those aspects that will be needed in subsequent chapters. The study of these fields, and their interaction with other branches of mathematics forms a vast area of current research.
Kenneth Ireland, Michael Rosen
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In this chapter we shall introduce the concept of an algebraic number field and develop its basic properties. Our treatment will be classical, developing directly only those aspects that will be needed in subsequent chapters. The study of these fields, and their interaction with other branches of mathematics forms a vast area of current research.
Kenneth Ireland, Michael Rosen
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Algebraic properties of number theories
Israel Journal of Mathematics, 1975Among other things we prove the following. (A) A number theory is convex if and only if it is inductive. (B) No r.e. number theory has JEP. (C) No number theory has AP. We also give some information about the hard cores of number theories.
H. Simmons +3 more
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2002
Public-key cryptosystems are based on modular arithmetic. In this section, we summarize the concepts and results from algebra and number theory which are necessary for an understanding of the cryptographic methods. Textbooks on number theory and modular arithmetic include [HarWri79], [IreRos82], [Rose94], [Forster96] and [Rosen2000].
Helmut Knebl, Hans Delfs
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Public-key cryptosystems are based on modular arithmetic. In this section, we summarize the concepts and results from algebra and number theory which are necessary for an understanding of the cryptographic methods. Textbooks on number theory and modular arithmetic include [HarWri79], [IreRos82], [Rose94], [Forster96] and [Rosen2000].
Helmut Knebl, Hans Delfs
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Algebraic groups and number theory
Russian Mathematical Surveys, 1992This article is made up of the material of the Soviet-American symposium ``Algebraic groups and number theory'' which took place from 22-29 May 1991 in Minsk. The scientific programme covered current problems in the arithmetic theory of algebraic groups, the theory of discrete subgroups of Lie groups, algebraic geometry, and number theory.
Platonov, V. P., Rapinchuk, A. S.
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A Development of Associative Algebra and an Algebraic Theory of Numbers, I
Mathematics Magazine, 1952in which if we denote a particular element by Ck, its immediate successor in this is CkJ, where k denotes a natural number and k' its immediate successor in the set of natural numbers. We then introduced in addition to these symbols the symbol + (called a plus sign); x (called a multiplication sign); and (, called a left parenthesis symbol; and ...
M. W. Weaver, H. S. Vandiver
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