scholarly journals Deception as a Derived Function of Language

2016 ◽  
Vol 7 ◽  
Author(s):  
Nathan Oesch
Keyword(s):  
Derived Function

scholarly journals Understanding the structure-derived function of metal–organic frameworks and their application in separations

2019 ◽  
Vol 75 (a2) ◽  
pp. e511-e511
Author(s):  
Mehrdad Asgari ◽  
Ilia Kochetygov ◽  
Matthew Hudson ◽  
Jeffrey R. Long ◽  
Craig Brown ◽  
...  
Keyword(s):  
Metal Organic Frameworks ◽  
Metal Organic ◽  
Derived Function

I. On the conditions for the existence of three equal roots, or of two pairs of equal roots of a binary quartic or quintic

1868 ◽  
Vol 16 ◽  
pp. 229-229
Keyword(s):  
Single Equation ◽  
The Other ◽  
Two Component ◽  
Composition Of Relations ◽  
Derived Function

In considering the conditions for the existence of given systems of equalities between the roots of an equation, we obtain some very interesting examples of the composition of relations. A relation is either onefold, expressed by a single equation U = 0, or it is, say, k -fold, expressed by a system of k or more equations. Of course, as regards onefold relations, the theory of the composition is well known: the relation UV = 0 is a relation compounded of the relations U = 0, V = 0 ; that is, it is a relation satisfied if, and not satisfied unless one or the other of the two component relations is satisfied. The like notion of composition applies to relations in general; viz., the compound relation is a relation satisfied if, and not not satisfied unless one or the other of the two component relations is satisfied. The author purposely refrains at present from any further discussion of the theory of composition. The conditions for the existence of given systems of equalities between the roots of an equation furnish instances of such composition; in fact, if we express that the function (*) ( x, y ) n and its first-derived function in regard to x , or, what is the same thing, the first-derived functions in regard to x, y respectively, have a common quadric factor, we obtain between the coefficients a certain twofold relation, which implies either that the equation (*)( x ,y ) n = 0 has three equal roots, or else that it has two pairs of equal roots; that is, the relation in question is satisfied if, and it is not satisfied unless there is satisfied either the relation for the existence of three equal roots, or else the relation for the existence of two pairs of equal roots; or the relation for the quadric factor is compounded of the last-mentioned two relations. The relation for the quadric factor, for any value whatever of n , is at once seen to be expressible by means of an oblong matrix, giving rise to a series of determinants which are each to be put = 0; the relation for three equal roots and that for two pairs of equal roots in the particular cases n = 4 and n = 5, are given in the author’s "Memoir on the Conditions for the existence of given Systems of Equalities between the roots of an Equation, Phil. Trans, t. cxlvii. (1857), pp. 727-731; and he proposes in the present Memoir to exhibit, for the cases in question n = 4 and n = 5, the connexion between the compound relation for the quadric factor and the component relations for the three equal roots and for the two pairs of equal roots respectively.

Proposal and validation of polyconvex strain-energy function for biological soft tissues

2021 ◽  
pp. 1-14
Author(s):  
Takashi Funai ◽  
Hiroyuki Kataoka ◽  
Hideo Yokota ◽  
Taka-aki Suzuki
Keyword(s):  
Curve Fitting ◽  
Energy Function ◽  
Strain Energy ◽  
Soft Tissues ◽  
Strain Energy Function ◽  
Biological Tissues ◽  
Stress Strain ◽  
Increasing Trend ◽  
Strain Energy Functions ◽  
Derived Function

BACKGROUND: Mechanical simulations for biological tissues are effective technology for development of medical equipment, because it can be used to evaluate mechanical influences on the tissues. For such simulations, mechanical properties of biological tissues are required. For most biological soft tissues, stress tends to increase monotonically as strain increases. OBJECTIVE: Proposal of a strain-energy function that can guarantee monotonically increasing trend of biological soft tissue stress-strain relationships and applicability confirmation of the proposed function for biological soft tissues. METHOD: Based on convexity of invariants, a polyconvex strain-energy function that can reproduce monotonically increasing trend was derived. In addition, to confirm its applicability, curve-fitting of the function to stress-strain relationships of several biological soft tissues was performed. RESULTS: A function depending on the first invariant alone was derived. The derived function does not provide such inappropriate negative stress in the tensile region provided by several conventional strain-energy functions. CONCLUSIONS: The derived function can reproduce the monotonically increasing trend and is proposed as an appropriate function for biological soft tissues. In addition, as is well-known for functions depending the first invariant alone, uniaxial-compression and equibiaxial-tension of several biological soft tissues can be approximated by curve-fitting to uniaxial-tension alone using the proposed function.

Design and Research on Optimization Combination of UWB Pulse Waveform Based on Gaussian Pulse Derived Function

2013 ◽  
Vol 427-429 ◽  
pp. 1995-1998
Author(s):  
Xue Wen He ◽  
Sun Han ◽  
Kuan Gang Fan ◽  
Ying Fei Sheng ◽  
Qing Mei Cao
Keyword(s):  
Spectral Density ◽  
Linear Combination ◽  
Pulse Signal ◽  
Federal Communications Commission ◽  
Ultra Wideband ◽  
Gaussian Pulse ◽  
Spectrum Utilization ◽  
Energy Spectral Density ◽  
Different Order ◽  
Derived Function

This paper analyses time-domain waveform and its unilateral energy spectral density based on the Gaussian pulse former 12 derivative functions. We could conclude that pulse forming factor has a closer relationship with different order number derived function affected the energy spectral density. Therefore, in order to maximize the approximate Federal Communications Commission (FCC) emission mask as much as possible, an iterative algorithm is proposed to optimize the linear combination of the Gaussian pulse former 12 order derived function. Compared with single differential Gaussian pulse, the simulation results show that after linear combination, new ultra-wideband pulse signal could greatly meet the spectrum utilization and indoor radiation mask standards promulgated by the FCC.

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