On a Noncompact Minimization Problem of Hardy-Sobolev Type

2002 ◽  
Vol 2 (1) ◽  
Author(s):  
K. Sandeep
Keyword(s):  
Minimization Problem ◽  
Sobolev Type ◽  
Existence And Nonexistence ◽  
Constraint Minimization

AbstractIn this paper we discuss the existence and nonexistence of minimizer for the constraint minimization problem

scholarly journals On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Mohaemd Jleli ◽  
Bessem Samet
Keyword(s):  
Critical Exponent ◽  
Weak Solutions ◽  
Fractional Derivatives ◽  
Sobolev Type ◽  
Existence And Nonexistence

We consider two fractional in time nonlinear Sobolev-type inequalities involving potential terms, where the fractional derivatives are defined in the sense of Caputo. For both problems, we study the existence and nonexistence of nontrivial local weak solutions. Namely, we show that there exists a critical exponent according to which we have existence or nonexistence.

A Vectorized Regularization Method for Multivalued Parameters Identification

2019 ◽  
Vol 16 (07) ◽  
pp. 1850110 ◽  
Author(s):  
Abdellatif Ellabib ◽  
Youssef Ouakrim
Keyword(s):  
Minimization Problem ◽  
Regularization Method ◽  
Dual Problem ◽  
Conjugate Functions ◽  
Primal Problem ◽  
Dispersion Tensor ◽  
Qualification Conditions ◽  
Primal Dual ◽  
Constraint Minimization ◽  
Stability Of The Solution

The identification of multivalued parameters is formulated as a constraint minimization problem called primal problem. We embed it in a family of perturbed problems and we associate a dual problem with it using the conjugate functions. Basing on the primal-dual relationship, under some qualification conditions on the parameters to be identified we elaborate the well posedeness, convergence and stability of the solution assuming. Numerical simulations are described in the end for the identification of discontinuous dispersion tensor in transport equations.

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Being and Reason

2019 ◽  
Author(s):  
Martin Lin
Keyword(s):  
Sufficient Reason ◽  
Existence Of God ◽  
Principle Of Sufficient Reason ◽  
Existence And Nonexistence ◽  
New Interpretation ◽  
Necessary Existence

In Being and Reason, Martin Lin offers a new interpretation of Spinoza’s core metaphysical doctrines with attention to how and why, in Spinoza, metaphysical notions are entangled with cognitive, logical, and epistemic ones. For example, according to Spinoza, a substance is that which can be conceived through itself, and a mode is that which is conceived through another. Thus, metaphysical notions, substance and mode, appear to be defined through a notion that is either cognitive or logical, being conceived through. What are we to make of the intimate connections that Spinoza sees between metaphysical, cognitive, logical, and epistemic notions? Or between being and reason? Lin argues against idealist readings according to which the metaphysical is reducible to or grounded in something epistemic, logical, or psychological. He maintains that Spinoza sees the order of being and the order of reason as two independent structures that mirror one another. In the course of making this argument, he develops new interpretations of Spinoza’s notions of attribute and mode, and of Spinoza’s claim that all things strive for self-preservation. Lin also argues against prominent idealist readings of Spinoza according to which the Principle of Sufficient Reason is absolutely unrestricted for Spinoza and is the key to his system. He contends, rather, that Spinoza’s metaphysical rationalism is a diverse phenomenon and that the Principle of Sufficient Reason is limited to claims about existence and nonexistence which are applied only once by Spinoza to the case of the necessary existence of God.

scholarly journals Optimal Energy Beamforming to Minimize Transmit Power in a Multi-Antenna Wireless Powered Communication Network

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 509
Author(s):  
Iqra Hameed ◽  
Pham-Viet Tuan ◽  
Mario R. Camana ◽  
Insoo Koo
Keyword(s):  
Communication Network ◽  
Minimization Problem ◽  
Time Allocation ◽  
Access Point ◽  
Power Minimization ◽  
Transmit Power ◽  
Optimal Energy ◽  
Single Antenna ◽  
Information Signal ◽  
Energy Beamforming

In this paper, we study the transmit power minimization problem with optimal energy beamforming in a multi-antenna wireless powered communication network (WPCN). The considered network consists of one hybrid access point (H-AP) with multiple antennae and multiple users with a single antenna each. The H-AP broadcasts an energy signal on the downlink, using energy beamforming to enhance the efficiency of the transmit energy. In this paper, we jointly optimize the downlink time allocation for wireless energy transfer (WET), the uplink time allocation for each user to send a wireless information signal to the H-AP, the power allocation to each user on the uplink, and the downlink energy beamforming vectors while controlling the transmit power at the H-AP. It is challenging to solve this non-convex complex optimization problem because it is numerically intractable and involves high computational complexity. We exploit a sequential parametric convex approximation (SPCA)-based iterative method, and propose optimal and sub-optimal solutions for the transmit power minimization problem. All the proposed schemes are verified by numerical simulations. Through the simulation results, we present the performance of the proposed schemes based on the effect of the number of transmit antennae and the number of users in the proposed WPCN. Through the performance evaluation, we show that the SPCA-based joint optimization solution performance is superior to other solutions.

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