搜索结果：Taylor

Using the recently defined concept of Taylor measures, we propose a generalization of Taylor's theorem to measurable, non-analytic functions, that do not require differentiation. We study consequences of the generalization, including the definition and properties of a new space of functions, which will be called multivariate Taylor measure function space. The proposed generalization emerges as a unifying framework that includes many concepts from mathematics as special cases.

We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We illustrate, through examples, how the deterministic and stochastic versions of the proposed Taylor measures emerge as a unifying framework that includes many concepts from mathematics and probability theory as special cases.

First discovered by L. R. Taylor (1961, Nature), Taylor's Power Law (TPL) correlates the mean (M) population abundances and the corresponding variances (V) across a set of insect populations using a power function (V=aM^b). TPL has demonstrated its 'universality' across numerous fields of sciences, social sciences, and humanities. This universality has inspired two main prongs of exploration: one from mathematicians and statisticians, who might instinctively respond with a convergence theorem similar to the central limit theorem of the Gaussian distribution, and another from biologists, ecologists, physicists, etc., who are more interested in potential underlying ecological or organizational mechanisms. Over the past six decades, TPL studies have produced a punctuated landscape with three relatively distinct periods (1960s-1980s; 1990s-2000s, and 2010s-2020s) across the two prongs of abstract and physical worlds. Eight themes have been identified and reviewed on this landscape, including population spatial aggregation and ecological mechanisms, TPL and skewed statistical distributions, mathematical/statistical mechanisms of TPL, sample vs. population TPL, population stability, sync

We prove classical Taylor polynomial theorems for sub-Riemannian manifolds that are obtained as the submetric image of a Carnot group. For these theorems we also prove a sufficient condition for real analyticity and a result on L-harmonicity of Taylor polynomials.

In the paper we investigate the joint spectra of Banach space representations of the quantum q-plane called Banach q-modules. Based on the transversality relation from the topological homology of the trivial modules versus given a left Banach q-module, we introduce the joint (essential) spectra of a Banach q-module. In particular, we have the well defined Taylor joint spectrum of a Banach q-module. The noncommutative projection q-property is proved for the Taylor spectrum, which stands out the conventional projection property in the commutative case. It is provided the key examples of the Banach q-modules, which do not possesses nether forward nor backward projection properties.

A polynomial homotopy is a family of polynomial systems in one parameter, which defines solution paths starting from known solutions and ending at solutions of a system that has to be solved. We consider paths leading to isolated singular solutions, to which the Taylor series converges logarithmically. Whether or not extrapolation algorithms manage to accelerate the slowly converging series depends on the proximity of poles close to the disk of convergence of the Taylor series.

We develop a general transfer-matrix formalism for determining the growth rate of the Rayleigh-Taylor instability in a fluid system with spatially varying density and viscosity. We use this formalism to analytically and numerically treat the case of a stratified heterogeneous fluid. We introduce the inviscid-flow approximation in our transfer-matrix formalism to find analytic solutions in the limit of uniform kinematic viscosity for a stratified heterogeneous fluid. We discuss the applicability of these results and the no-acceleration approximation that also yields analytical solutions in the large viscosity limit.

A concise review is given of astrophysically motivated experimental and theoretical research on Taylor-Couette flow. The flows of interest rotate differentially with inner cylinder faster than outer one but are linearly stable against Rayleigh's inviscid centrifugal instability. At shear Reynolds numbers as large as 10^6, hydrodynamic flows of this type (quasi-keplerian) appear to be nonlinearly stable: no turbulence is seen that cannot be attributed to interaction with the axial boundaries, rather than the radial shear itself. Direct numerical simulations agree, although they cannot yet reach such high Reynolds numbers. This result indicates that accretion-disc turbulence is not purely hydrodynamic in origin, at least insofar as it is driven by radial shear. Theory, however, predicts linear magnetohydrodynamic (MHD) instabilities in astrophysical discs: in particular, the standard magnetorotational instability (SMRI). MHD Taylor-Couette experiments aimed at SMRI are challenged by the low magnetic Prandtl numbers of liquid metals. High fluid Reynolds numbers and careful control of the axial boundaries are required. The quest for laboratory SMRI has been rewarded with the discovery

Muscle tissue drives nearly all movement in the animal kingdom, providing power, mobility, and dexterity. Technologies for measuring muscle tissue motion, such as sonomicrometry, fluoromicrometry, and ultrasound, have significantly advanced our understanding of biomechanics. Yet, the field lacks the ability to monitor muscle tissue motion for animal behavior outside the lab. Towards addressing this issue, we previously introduced magnetomicrometry, a method that uses magnetic beads to wirelessly monitor muscle tissue length changes, and we validated magnetomicrometry via tightly-controlled in situ testing. In this study we validate the accuracy of magnetomicrometry against fluoromicrometry during untethered running in an in vivo turkey model. We demonstrate real-time muscle tissue length tracking of the freely-moving turkeys executing various motor activities, including ramp ascent and descent, vertical ascent and descent, and free roaming movement. Given the demonstrated capacity of magnetomicrometry to track muscle movement in untethered animals, we feel that this technique will enable new scientific explorations and an improved understanding of muscle function. -- -- El tejido m

The multi-point Taylor polynomial, which is the general, unique and of minimum degree ($mk+m-1$) polynomial $P_{k,m}(x)$ which interpolates a function's derivatives in multiple points is presented in its explicit form. A proof that this expression satisfies the multi-point Taylor polynomial's defining property is given. Namely, it is proven that for a k-differentiable function $f$ and a set of different m-points $\{a_1,...,a_m\}$, this polynomial satisfies $P^{(n)}_{k,m}(a_i) = f^{(n)}(a_i)\quad \forall \, i = 1,...,m\quad \&\quad \forall \, n = 0,...,k$. A discussion regarding previous expressions presented in the literature, which mostly consisted in recursion formulas and not explicit formulas, is made.

Taylor Farms stirred confusion on FDA test and provided a vague recall list

Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a generalized Newton iteration method derived from the generalized local fractional Taylor series with the local fractional derivatives is reviewed. Operators on real line numbers on a fractal space are induced from Cantor set to fractional set. Existence for a generalized fixed point on generalized metric spaces may take place.

Current techniques for explainable AI have been applied with some success to image processing. The recent rise of research in video processing has called for similar work n deconstructing and explaining spatio-temporal models. While many techniques are designed for 2D convolutional models, others are inherently applicable to any input domain. One such body of work, deep Taylor decomposition, propagates relevance from the model output distributively onto its input and thus is not restricted to image processing models. However, by exploiting a simple technique that removes motion information, we show that it is not the case that this technique is effective as-is for representing relevance in non-image tasks. We instead propose a discriminative method that produces a naïve representation of both the spatial and temporal relevance of a frame as two separate objects. This new discriminative relevance model exposes relevance in the frame attributed to motion, that was previously ambiguous in the original explanation. We observe the effectiveness of this technique on a range of samples from the UCF-101 action recognition dataset, two of which are demonstrated in this paper.

The equation of state (EoS), quark number density and susceptibility at nonzero quark chemical potential $μ$ are studied in lattice QCD simulations with a clover-improved Wilson fermion of 2-flavors and RG-improved gauge action. To access nonzero $μ$, we employ two methods : a multi-parameter reweighting (MPR) in $μ$ and $β$ and Taylor expansion in $μ/T$. The use of a reduction formula for the Wilson fermion determinant enables to study the reweighting factor in MPR explicitly and heigher-order coefficients in Taylor expansion free from errors of noise method, although calculations are limited to small lattice size. As a consequence, we can study the reliability of the thermodynamical quantities through the consistency of the two methods, each of which has different origin of the application limit. The thermodynamical quantities are obtained from simulations on a $8^3\times 4$ lattice with an intermediate quark mass($m_{\rm PS}/m_{\rm V}=0.8)$. The MPR and Taylor expansion are consistent for the EoS and number density up to $μ/T\sim 0.8$ and for the number susceptibility up to $μ/T \sim 0.6$. This implies within a given statistics that the overlap problem for the MPR and truncation