Search results for "Exponential function"
showing 10 items of 173 documents
What is the best fitting function? Evaluation of lactate curves with common methods from the literature
2015
Using the lactate threshold for training prescription is the gold-standard, although there are several open questions. One open question is: What is the best fitting method for the load-lactate data points? This investigation re-analyses over 3500 lactate diagnostic datasets in swimming. Our evaluation software examines six different fitting methods with two different minimization criteria (RMSE and SE). Optimization of parameters of the functions is put in excecution with gradient descent. From a mathematical point of view, the double phase model, which consists of two linear regression lines, shows the least errors (RMSE min 0.254 ± 0.172; SE min 0.311 ± 0.210). However, this method canno…
High-field nuclear spin relaxation in liquids and solids
1990
The authors generalise the standard theory of nuclear spin relaxation to situations in which the Markovian approximation is not applicable. Expressions for generalised frequency-dependent spin relaxation functions are presented. They show that under high-field conditions the relaxation of longitudinal magnetisation is exponential independent of the particular time dependence of the correlation functions.
A Unifying Framework for Perturbative Exponential Factorizations
2021
We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed. A new lower bound for the convergence of theWilcox expansion is provided, as well as some applications of the results. In particular, two examples are worked out up to a high order of approximation to illustrate the behavior of the Wilcox expansion.
<title>Relaxation processes in amorphous As-S and As-Se films</title>
1997
The relaxation of optical, mechanical and chemical properties of as-evaporated amorphous As-S and As-Se films while storing them at room temperature is investigated. The AsxS1-x films with arsenic content 0.3 less than x less than 0.4 are found to undergo maximal changes. It is shown that the phenomenon of dark self-enhancement of holograms (an increase of diffraction efficiency over time without any special treatment) can be used as an efficient method for investigation of relaxation processes in the amorphous chalcogenide films. The changes of diffraction efficiency in amorphous As2S3 films have been measured as a function of aging time and recording light intensity. The relaxation proces…
Sensitivity Versus Certificate Complexity of Boolean Functions
2016
Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been notoriously hard to obtain even exponential bounds. Since block sensitivity is known to be polynomially related to certificate complexity, an equivalent of proving this conjecture would be showing that the certificate complexity is polynomially related to sensitivity. Previously, it has been shown that $$bsf \le Cf \le 2^{sf-1} sf - sf-1$$. In this work, we give a better upper bound of $$bsf \le Cf \le \max \left 2^{sf-1}\left sf-\frac{1}{3}\right , sf\right $…
TIGHT BOUNDS FOR THE SPACE COMPLEXITY OF NONREGULAR LANGUAGE RECOGNITION BY REAL-TIME MACHINES
2013
We examine the minimum amount of memory for real-time, as opposed to one-way, computation accepting nonregular languages. We consider deterministic, nondeterministic and alternating machines working within strong, middle and weak space, and processing general or unary inputs. In most cases, we are able to show that the lower bounds for one-way machines remain tight in the real-time case. Memory lower bounds for nonregular acceptance on other devices are also addressed. It is shown that increasing the number of stacks of real-time pushdown automata can result in exponential improvement in the total amount of space usage for nonregular language recognition.
Star-polynomial identities: computing the exponential growth of the codimensions
2017
Abstract Can one compute the exponential rate of growth of the ⁎-codimensions of a PI-algebra with involution ⁎ over a field of characteristic zero? It was shown in [2] that any such algebra A has the same ⁎-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth e x p ⁎ ( A ) of any PI-algebra A with involution. It turns out that e x p ⁎ ( A ) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.
Proper identities, Lie identities and exponential codimension growth
2008
Abstract The exponent exp ( A ) of a PI-algebra A in characteristic zero is an integer and measures the exponential rate of growth of the sequence of codimensions of A [A. Giambruno, M. Zaicev, On codimension growth of finitely generated associative algebras, Adv. Math. 140 (1998) 145–155; A. Giambruno, M. Zaicev, Exponential codimension growth of P.I. algebras: An exact estimate, Adv. Math. 142 (1999) 221–243]. In this paper we study the exponential rate of growth of the sequences of proper codimensions and Lie codimensions of an associative PI-algebra. We prove that the corresponding proper exponent exists for all PI-algebras, except for some algebras of exponent two strictly related to t…
Size of Quantum Finite State Transducers
2007
Sizes of quantum and deterministic finite state transducers are compared in the case when both quantum and deterministic finite state transducers exist. The difference in size may be exponential.
On Finite Satisfiability of the Guarded Fragment with Equivalence or Transitive Guards
2007
The guarded fragment of first-order logic, GF, enjoys the finite model property, so the satisfiability and the finite satisfiability problems coincide. We are concerned with two extensions of the two-variable guarded fragment that do not possess the finite model property, namely, GF2 with equivalence and GF2 with transitive guards. We prove that in both cases every finitely satisfiable formula has a model of at most double exponential size w.r.t. its length. To obtain the result we invent a strategy of building finite models that are formed from a number of multidimensional grids placed over a cylindrical surface. The construction yields a 2NEXPTIME-upper bound on the complexity of the fini…