A note on the derivation of the derivatives of invariants of stretch tensor to the right Cauchy-Green*

2006 ◽  
Vol 16 (1) ◽  
pp. 96-99
Author(s):  
Tian Dongyan ◽  
Jin Ming ◽  
Dui Guansuo
Keyword(s):  
Stretch Tensor ◽  
The Right ◽  
Derivatives Of

scholarly journals An exact formulation for exponential-logarithmic transformation stretches in a multiphase phase field approach to martensitic transformations

2020 ◽  
Vol 25 (6) ◽  
pp. 1219-1246 ◽  
Author(s):  
Anup Basak ◽  
Valery I Levitas
Keyword(s):  
Phase Field ◽  
Kinematic Model ◽  
Martensitic Transformations ◽  
Order Parameters ◽  
Field Approach ◽  
Natural Logarithm ◽  
Stretch Tensor ◽  
Second Derivatives ◽  
Derivatives Of ◽  
Martensitic Variants

A general theoretical and computational procedure for dealing with an exponential-logarithmic kinematic model for transformation stretch tensor in a multiphase phase field approach to stress- and temperature-induced martensitic transformations with N martensitic variants is developed for transformations between all possible crystal lattices. This kinematic model, where the natural logarithm of transformation stretch tensor is a linear combination of natural logarithm of the Bain tensors, yields isochoric variant–variant transformations for the entire transformation path. Such a condition is plausible and cannot be satisfied by the widely used kinematic model where the transformation stretch tensor is linear in Bain tensors. Earlier general multiphase phase field studies can handle commutative Bain tensors only. In the present treatment, the exact expressions for the first and second derivatives of the transformation stretch tensor with respect to the order parameters are obtained. Using these relations, the transformation work for austenite ↔ martensite and variant ↔ variant transformations is analyzed and the thermodynamic instability criteria for all homogeneous phases are expressed explicitly. The finite element procedure with an emphasis on the derivation of the tangent matrix for the phase field equations, which involves second derivatives of the transformation deformation gradients with respect to the order parameters, is developed. Change in anisotropic elastic properties during austenite–martensitic variants and variant–variant transformations is taken into account. The numerical results exhibiting twinned microstructures for cubic to orthorhombic and cubic to monoclinic-I transformations are presented.

Approximations by multivariate perturbed neural network operators

2017 ◽  
Vol 15 (03) ◽  
pp. 413-432 ◽  
Author(s):  
George A. Anastassiou
Keyword(s):  
Neural Network ◽  
Rate Of Convergence ◽  
Activation Function ◽  
Jackson Type ◽  
Partial Derivatives ◽  
Right Hand ◽  
Hidden Layer ◽  
The Right ◽  
Derivatives Of

This article deals with the determination of the rate of convergence to the unit of each of three newly introduced here multivariate perturbed normalized neural network operators of one hidden layer. These are given through the multivariate modulus of continuity of the involved multivariate function or its high-order partial derivatives and that appears in the right-hand side of the associated multivariate Jackson type inequalities. The multivariate activation function is very general, especially it can derive from any multivariate sigmoid or multivariate bell-shaped function. The right-hand sides of our convergence inequalities do not depend on the activation function. The sample functionals are of multivariate Stancu, Kantorovich and quadrature types. We give applications for the first partial derivatives of the involved function.

A preclinical survey on the efficacy of NSC-290205 in combination with doxorubicin (ADR) in Lewis lung carcinoma (LLC)

2006 ◽  
Vol 24 (18_suppl) ◽  
pp. 17131-17131
Author(s):  
A. Papageorgiou ◽  
E. Stergiou ◽  
I. Boukovinas ◽  
G. Geromichalos ◽  
I. Stergiou
Keyword(s):  
Antitumor Activity ◽  
Tumor Growth ◽  
Maximum Effect ◽  
Base Pairs ◽  
Chop Regimen ◽  
C57bl Mice ◽  
Inhibition Of Tumor Growth ◽  
Reduced Toxicity ◽  
The Right ◽  
Derivatives Of

17131 Background: NSC-290205 (A) is a hybrid synthetic antitumor ester, which combines a D-lactam derivative of androsterone and nitrogen mustard. Studies on modified steroidal esters of carboxylic derivatives of N,N-bis(2-chloroethyl)aniline, have shown that they exhibit reduced toxicity and increased antitumor activity and specificity. In this study we investigated the antitumor activity of compound A in combination with ADR (AHOP) in comparison with standard CHOP regimen. Methods: C57Bl mice were used for the antitumor evaluation of AHOP/CHOP. Experiments were initiated by implanting the tumor. LLC cells (purchased by NCI, Bethesda, USA) were implanted intramuscularly into the right hind leg as a suspension of 7 × 106 cells in 0.1 ml. The antitumor activity was assessed from the inhibition of tumor growth by volume in cm3 and the oncostatic parameter T/C % according to the protocol of experimental evaluation of antitumor drugs of the NCI, USA. Treatments were given as a single dose (D) on day 1, intermitted dose (D/2 × 3) on days 1, 5, 9 or consecutive dose (D/4 × 9) on days 1 through 9. Results: Treatment with A or cyclophosphamide produced almost equal borderline activity. Moreover, both CHOP and AHOP regimens showed significant and comparable antitumor effect (p < 0.05 by the Wilkoxon test). AHOP caused the maximum effect inhibiting the tumor growth by 67.7% and T/C values of 270%. CHOP was less effective producing 54.8% tumor inhibition and T/C values of 238%. Conclusions: It is very likely that the D-lactamic steroid (androstan) alkylator for A, containing the -NHCO group, combined with ADR, which intercalates between base-pairs, is the explanation for higher activity of AHOP vs. CHOP. This significant effect of NSC-290205 with the anthracycline adriamycin on LLC adds to NSC-290205 advantage for further clinical development. No significant financial relationships to disclose.

scholarly journals ON SMOOTHNESS OF SOLUTION OF ONE NONLOCAL PROBLEM FOR HYPERBOLIC EQUATION

2021 ◽  
Vol 26 (2) ◽  
pp. 15-22
Author(s):  
V. A. Kirichek
Keyword(s):  
Hyperbolic Equation ◽  
Nonlocal Problem ◽  
Generalized Solution ◽  
Integral Boundary ◽  
Apriori Estimates ◽  
The Space L2 ◽  
Elastic Fixation ◽  
The Right ◽  
Derivatives Of ◽  
Smoothness Of Solution

In this paper we consider a nonlocal problem with integral boundary condition for hyperbolic equation. The conditions of the problem contain derivatives of the first order with respect to both x and t,, which can be interpreted as an elastic fixation of the right end rod in the presence of a certain damper, and since the conditions also contain integral of the desired solution, this condition is nonlocal. It is known that problems with nonlocal integral conditions are non-self-adjoint and, therefore, the study of solvability encounters difficulties that are not characteristic of self-adjoint problems. Additional difficulties arise also due to the fact that one of the conditions is dynamic. The attention of the article is focused on studying thesmoothness of the solution of the nonlocal problem. The concept of a generalized solution is introduced, and the existence of second-order derivatives and their belonging to the space L2 are proved. The proof is basedon apriori estimates obtained in this work.

General Derivations for Conjugate Strains of Eshelby-Like Stress Tensors

Volume 1 ◽  
2004 ◽  
Author(s):  
K. Behfar ◽  
A. Sheshmani ◽  
R. Naghdabadi
Keyword(s):  
Stress Tensor ◽  
General Class ◽  
General Type ◽  
Principal Axis ◽  
Stretch Tensor ◽  
Stress Tensors ◽  
Definition Of ◽  
General Relations ◽  
The Right ◽  
Conjugate Stress

In this paper, a general type of Eshelby-like stress tensor is defined which is based on the right stretch tensor and is equal to the product of a general class of strain and the corresponding conjugate stress tensor. The Eshelby-like stress tensor depending on the fact that from which side the stress tensor is multiplied by, is categorized into the right-weighted and left-weighted ones. General relations for conjugate strains of Eshelby-like stress tensors are investigated using the method, based on the definition of energy conjugacy and Hill’s principal axis method.

EVOLUTION OF TRANSPOSONS: NATURAL SELECTION FOR Tn5 IN ESCHERICHIA COLI K12

Genetics ◽  
1983 ◽  
Vol 103 (4) ◽  
pp. 581-592
Author(s):  
Susan Wurster Biel ◽  
Daniel L Hartl
Keyword(s):  
Escherichia Coli ◽  
Growth Rate ◽  
Rate Effect ◽  
Coding Region ◽  
Bacterial Populations ◽  
The Right ◽  
Derivatives Of ◽  
Intact Element ◽  
Prior Adaptation

ABSTRACT A novel in vivo effect of the transposable element Tn5 has been observed in chemostats when certain isogenic Tn5 and non-Tn5 strains of Escherichia coli compete for a limiting carbon source in the absence of kanamycin. The Tn5-bearing strain has a more rapid growth rate and increases in frequency from 50% to 90% within the first 15 to 20 generations. The effect occurs when Tn5 is inserted at a variety of chromosomal locations or when the element is carried by an episome, but it is strain specific, having been observed in two out of three strains examined. (For reasons unknown, the effect has not been observed with derivatives of strain CSH12.) Although the growth-rate advantage of Tn5 is independent of nutrient concentration and generation time, it can be reduced by prior adaptation of the strains to limiting conditions, and the amount of reduction is proportional to the length of prior adaptation. The growth-rate effect is evidently not caused by beneficial mutations induced by Tn5 transposition, as Tn5-bearing strains selected in chemostats retain their initial Tn5 position and copy number. However, the effect does not occur in Tn5-112, a transpositionless deletion mutation missing the transposase-coding region of the right-hand IS sequence flanking the element. Since Tn5-112 retains a functional kanamycin-phosphotransferase gene, this gene is not responsible for the growth-rate effect. Thus, the effect evidently requires transposase function, but it does not involve actual transposition of the intact element. Altogether, these data provide a mechanism for the maintenance of Tn5 in bacterial populations in the absence of kanamycin, and they suggest a model for the proliferation and the maintenance of IS sequences and transposable elements in the absence of other identifiable selection pressures.

Thermodynamic Identities

2019 ◽  
pp. 165-183
Author(s):  
Robert H. Swendsen
Keyword(s):  
Thermodynamic Quantities ◽  
Partial Derivatives ◽  
Second Derivatives ◽  
Need To Evaluate ◽  
The Right ◽  
Derivatives Of

Many of the calculations in thermodynamics concern the effects of small changes. To carry out such calculations, we often need to evaluate first and second partial derivatives of some thermodynamic quantities with respect to other thermodynamic quantities. Although there are many such partial second derivatives, they are related by thermodynamic identities. This chapter explains the most straightforward way of deriving the needed thermodynamic identities. After explaining the derivation of Maxwell relations and how to find the right one for any given problem, Jacobian methods are introduced, with an accolade to their simplicity and utility. Several examples of the derivation of thermodynamic identities are given, along with a systematic guide for solving general problems.

scholarly journals Identification of a novel inhibitor for the Bromodomain (BRD4) through a receptor-based drug discovery approach

2020 ◽  
Vol 11 (3) ◽  
pp. 4359-4364
Author(s):  
Arivukkarasi Varadharajan ◽  
Raman Rajeshkumar ◽  
Chandrasekar MJN
Keyword(s):  
Molecular Docking ◽  
Drug Discovery ◽  
Molecular Level ◽  
Autodock Vina ◽  
Rule Violation ◽  
Docking Analysis ◽  
Novel Target ◽  
The Right ◽  
Almost All ◽  
Derivatives Of

Recently, the demands on the drug discovery process have increased drastically because of the need to apprehend a novel target which might be both pertinent to cause disease and chemically tractable. The emergence of bioinformatics and computer strategies have given room to analyse conditions at the molecular level. The present work was to perform a molecular docking analysis and ADMET study of different δ-carboline derivatives with bromodomain (BRD4) receptor using receptor-based drug discovery approach. Based on the literature, 60 compounds were designed and subjected to molecular docking for the inhibition of brd4 receptor. The results showed that Compound 34 received the highest binding affinity with BRD4 receptor. Hence eight compounds were selected based on docked pose determined using AutoDock/Vina with the minimal energy of above -5.1. Then ADMET study was carried, in that, all the eight compounds had middle to high BBB permeability. During metabolism, all compounds except compounds 37, 42 and 47 showed no inhibition of CYP2C99 in the liver. Analysis of drug-likeness profile showed almost all compounds eligible in CMC rule, violation rule of CMC, MDDR rule with the value of 1 and violations of WDI showed 0 value. Such findings strongly implied that derivatives of δ-carboline could serve as lead molecules to inhibit BRD4, and this could lead to the future development of the right candidate for cancer research.

scholarly journals Meiotic recombination on artificial chromosomes in yeast.

Genetics ◽  
1992 ◽  
Vol 131 (3) ◽  
pp. 541-550 ◽  
Author(s):  
L O Ross ◽  
D Treco ◽  
A Nicolas ◽  
J W Szostak ◽  
D Dawson
Keyword(s):  
Meiotic Recombination ◽  
Artificial Chromosome ◽  
Artificial Chromosomes ◽  
Crossover Behavior ◽  
Yeast Chromosome ◽  
Low Levels ◽  
Chromosome Iii ◽  
The Right ◽  
Yeast Artificial Chromosomes ◽  
Derivatives Of

Abstract We have examined the meiotic recombination characteristics of artificial chromosomes in Saccharomyces cerevisiae. Our experiments were carried out using minichromosome derivatives of yeast chromosome III and yeast artificial chromosomes composed primarily of bacteriophage lambda DNA. Tetrad analysis revealed that the artificial chromosomes exhibit very low levels of meiotic recombination. However, when a 12.5-kbp fragment from yeast chromosome VIII was inserted into the right arm of the artificial chromosome, recombination within that arm mimicked the recombination characteristics of the fragment in its natural context including the ability of crossovers to ensure meiotic disjunction. Both crossing over and gene conversion (within the ARG4 gene contained within the fragment) were measured in the experiments. Similarly, a 55-kbp region from chromosome III carried on a minichromosome showed crossover behavior indistinguishable from that seen when it is carried on chromosome III. We discuss the notion that, in yeast, meiotic recombination behavior is determined locally by small chromosomal regions that function free of the influence of the chromosome as a whole.

On Solving Certain Fractional Differential Equations With Right-Sided Derivatives

2009 ◽  
Author(s):  
Malgorzata Klimek
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Mellin Transform ◽  
Transform Method ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Meijer G Function ◽  
The Right ◽  
Derivatives Of

In the paper, solutions of basic fractional differential equations with right-sided derivatives of order α and with variable tβ - potential are derived using the Mellin transform method. The results are Meijer G-function series fulfilling the respective boundary conditions. The obtained series are transformed into solutions of analogous equations with left-sided derivatives and (b – t)β - potential. As an example case α + β = α/J is studied and for J = 1 the eigenfunctions of the right-sided Riemann-Liouville derivative are recovered.

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