A new principle for arbitrary meromorphic functions in a given domain

2018 ◽  
Vol 25 (2) ◽  
pp. 181-186 ◽  
Author(s):  
Grigor Barsegian
Keyword(s):  
Meromorphic Function ◽  
Lower Bounds ◽  
General Class ◽  
Meromorphic Functions ◽  
Upper Bounds ◽  
General Class Of Functions ◽  
Main Component ◽  
First Time ◽  
W Prime ◽  
Class Of Functions

Abstract This paper presents a new principle related to an arbitrary meromorphic function w in a given domain D. The main component of this principle gives (first time) lower bounds for {|w^{\prime}|} for a similar general class of functions. The principle can qualitatively be stated as follows: any set of simple a-points of w contains a “large” subset of complex values, where we have lower bounds for {|w^{\prime}|} and upper bounds for {|w^{(h)}|} , {h>1} .

A note on the age-dependent branching process with immigration

1975 ◽  
Vol 12 (01) ◽  
pp. 130-134 ◽  
Author(s):  
Norman Kaplan
Keyword(s):  
General Class ◽  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Direct Generalization ◽  
Age Dependent ◽  
General Class Of Functions ◽  
Branching Process With Immigration ◽  
Necessary And Sufficient ◽  
Class Of Functions

Let {Z(t)}t0be an age-dependent branching process with immigration. For a general class of functions Φ(x), a necessary and sufficient condition is given for whenE{Φ (Z(t))} <∞. This result is a direct generalization of a theorem proven for the branching process without immigration.

scholarly journals Fairness criteria for allocating scarce resources

2020 ◽  
Vol 14 (6) ◽  
pp. 1533-1541
Author(s):  
Bismark Singh
Keyword(s):  
Optimization Model ◽  
General Class ◽  
Fair Allocation ◽  
Scarce Resources ◽  
Multiple Resources ◽  
Multiple Users ◽  
Special Cases ◽  
General Class Of Functions ◽  
Class Of Functions

Abstract We develop an optimization model to provide a fair allocation of multiple resources to multiple users. All resources might not be suitable to all users. We develop a notion of fairness, and then provide a general class of functions achieving it. Next, we develop more restricted notions of fairness—special cases of which exist in literature. Finally, we distinguish between scarce and abundant resources, and show that if a resource is abundant, all users seeking it achieve the maximum possible coverage.

On the “Preconditioning” Function Used in Planewave DFT Calculations and its Generalization

2015 ◽  
Vol 18 (1) ◽  
pp. 167-179 ◽  
Author(s):  
Yunkai Zhou ◽  
James R. Chelikowsky ◽  
Xingyu Gao ◽  
Aihui Zhou
Keyword(s):  
Dft Calculations ◽  
General Formula ◽  
Significant Role ◽  
General Class ◽  
Order Approximation ◽  
Higher Order ◽  
Approximation Accuracy ◽  
General Class Of Functions ◽  
Class Of Functions

AbstractThe Teter, Payne, and Allan “preconditioning” function plays a significant role in planewave DFT calculations. This function is often called the TPA preconditioner. We present a detailed study of this “preconditioning” function. We develop a general formula that can readily generate a class of “preconditioning” functions. These functions have higher order approximation accuracy and fulfill the two essential “preconditioning” purposes as required in planewave DFT calculations. Our general class of functions are expected to have applications in other areas.

scholarly journals ON THE NUMBER OF LIMIT CYCLES IN PIECEWISE-LINEAR LIÉNARD SYSTEMS

2005 ◽  
Vol 15 (04) ◽  
pp. 1417-1422 ◽  
Author(s):  
A. TONNELIER
Keyword(s):  
Limit Cycles ◽  
General Class ◽  
Piecewise Linear ◽  
Liénard System ◽  
Liénard Systems ◽  
Lienard System ◽  
General Class Of Functions ◽  
Class Of Functions

In a previous paper [Tonnelier, 2002] we conjectured that a Liénard system of the form ẋ = p(x) - y, ẏ = x where p is piecewise linear on n + 1 intervals has up to 2n limit cycles. We construct here a general class of functions p satisfying this conjecture. Limit cycles are obtained from the bifurcation of the linear center.

On a problem of Chowla and some related problems

1936 ◽  
Vol 32 (4) ◽  
pp. 530-540 ◽  
Author(s):  
Paul Erdös
Keyword(s):  
General Class ◽  
Number Of Divisors ◽  
General Class Of Functions ◽  
Class Of Functions

Let d(m) denote the number of divisors of the integer m. Chowla has conjectured that the integers for which d(m + 1) > d(m) have density ½. In this paper I prove and generalize this conjecture. I prove in § 1 a corresponding result for a general class of functions f(m), and in § 2 the result for d(m) which is not included among the f(m). I employ the method used in my paper: “On the density of some sequences of numbers.”

A note on the age-dependent branching process with immigration

1975 ◽  
Vol 12 (1) ◽  
pp. 130-134 ◽  
Author(s):  
Norman Kaplan
Keyword(s):  
General Class ◽  
Branching Process ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Direct Generalization ◽  
Age Dependent ◽  
General Class Of Functions ◽  
Branching Process With Immigration ◽  
Necessary And Sufficient ◽  
Class Of Functions

Let {Z(t)}t0 be an age-dependent branching process with immigration. For a general class of functions Φ(x), a necessary and sufficient condition is given for when E{Φ (Z(t))} <∞. This result is a direct generalization of a theorem proven for the branching process without immigration.

Norm inequalities involving derivatives

1978 ◽  
Vol 82 (1-2) ◽  
pp. 51-70 ◽  
Author(s):  
W. D. Evans ◽  
A. Zettl
Keyword(s):  
General Class ◽  
New Method ◽  
Elementary Operator ◽  
Best Constant ◽  
New Approach ◽  
Theoretic Proof ◽  
General Class Of Functions ◽  
Image Position ◽  
Class Of Functions

SynopisisA new method for studying inequalities of the type ‖y(r)‖2<ε‖Sk−ry(k)‖2 + K(ε)‖S−ry‖2 and ‖y′‖2≦ Kp(S)‖Sy″‖ ‖S−1y‖ is presented here. With this new approach we obtain new and far reaching extensions of previously known inequalities of this sort as well as simpler proofs of the known cases. In addition we obtain an inequality of type ‖Sy′‖<ε‖(Sy′)′‖ + K(ε)‖y‖ for a general class of functions S. Also we give an elementary operator-theoretic proof of Everitt's characterization of the best constant as well as all cases of equality for

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