New insight into the Fourier-like and Darcy-like models in porous medium

In this study, we propose the general calculus operators based on the Richardson scaling law and Korcak scaling law. The Richardson-scaling-law calculus is considered to investigate the Fourier-like law for the scaling-law flow of the heat in the heat-transfer process. The Korcak-scaling-law calculus is used to model the Darcy-like law for describing the scaling-law flow of the fluid in porous medium. The formulas are as the special cases of the topology calculus proposed for descriptions of the fractal scaling-law behaviors in nature phenomena.

MOTIVIC EULER CHARACTERISTICS AND WITT-VALUED CHARACTERISTIC CLASSES

This paper examines Euler characteristics and characteristic classes in the motivic setting. We establish a motivic version of the Becker–Gottlieb transfer, generalizing a construction of Hoyois. Making calculations of the Euler characteristic of the scheme of maximal tori in a reductive group, we prove a generalized splitting principle for the reduction from $\operatorname{GL}_{n}$ or $\operatorname{SL}_{n}$ to the normalizer of a maximal torus (in characteristic zero). Ananyevskiy’s splitting principle reduces questions about characteristic classes of vector bundles in $\operatorname{SL}$-oriented, $\unicode[STIX]{x1D702}$-invertible theories to the case of rank two bundles. We refine the torus-normalizer splitting principle for $\operatorname{SL}_{2}$ to help compute the characteristic classes in Witt cohomology of symmetric powers of a rank two bundle, and then generalize this to develop a general calculus of characteristic classes with values in Witt cohomology.

New non-conventional methods for quantitative concepts of anomalous rheology

This paper addresses the general calculus operators with respect to another functions containg the power-law and exponential functions. The Boltzmann-type superposition principles for the anomalous linear viscoelasticity are considered for the first time. The new technologies are as non-conventional tools proposed to extend the quantitative concepts of anomalous rheology for solid mechanics.

Uji Validasi E-Module Matakuliah Kalkulus I untuk Mengoptimalkan Student Centered Learning dan Individual Learning Mahasiswa S-1

This research describes the validation calculus 1 e-module so as to optimize student centered learning and individual student learning S-1. This research uses descriptive research with 3 practitioner’s subject, and 20 students of S-1. Data collection technique used questionnaire rating scale e-module. This type of data is quantitative and qualitative data. The data analysis technique is descriptive analysis and reflective analysis. Expert assessment of design and media, e-module is expressed very valid with the validity of 90.07%. Expert assessment of content, e-modules otherwise very valid by the validity of 91.23%. E-module declared valid by an average of validity 88.55%. The trial results are limited small group of 20 students, e-module declared valid by the validity of 85.11%. In general, calculus 1 e-module course declared valid by an average of 89.01%, so it can be concluded decent e-module is used to optimize student centered learning and individual student learning S-1.

Deciding reachability problems in Turing-complete fragments of Mobile Ambients

The calculus of Mobile Ambients was proposed by Cardelli and Gordon as a foundational calculus for mobile computing. Since its introduction, the computational strength and the decidability of properties have been investigated for several fragments and variants of the standard calculus. We consider the problem of reachability and characterise a public (that is, restriction-free) fragment for which it is decidable. This fragment is obtained by removing the open capability and restricting the application of the replication operator to guarded processes only. This decidability result may appear surprising in combination with the fact that the same fragment was shown to be Turing complete by Maffeis and Phillips. Finally, we extend our decidability result in two ways: we first prove the decidability of a more general property called target reachability (according to which the target of interest for the reachability analysis consists of a possibly infinite set of processes) and then show that our decidability results also hold for a more general calculus, which includes the sophisticated communication mechanisms of Boxed Ambients, which is the most relevant variant of Mobile Ambients without the open capability.

MLP in Layer-Wise Form with Applications to Weight Decay

A simple and general calculus for the sensitivity analysis of a feedforward MLP network in a layer-wise form is presented. Based on the local optimality conditions, some consequences for the least-means-squares learning problem are stated and further discussed. Numerical experiments with formulation and comparison of different weight decay techniques are included.

A functional calculus for continuous affine operators

In the Appendix to a recent paper by J.J. Koliha and A.P. Leung (Math. Ann.216 (1975), 273–284), a functional calculus for continuous affine operators was constructed on the basis of the Taylor-Dunford calculus. This calculus applied only to functions defined and analytic in an open set containing the spectrum of an operator and the point λ = 1. In the present paper I examine the affine resolvent, and develop independently a more general calculus applicable to functions which are analytic in any open neighbourhood of the spectrum of an affine operator.