$$\alpha $$-Dirac-harmonic maps from closed surfaces

Abstract$$\alpha $$ α -Dirac-harmonic maps are variations of Dirac-harmonic maps, analogous to $$\alpha $$ α -harmonic maps that were introduced by Sacks–Uhlenbeck to attack the existence problem for harmonic maps from closed surfaces. For $$\alpha >1$$ α > 1 , the latter are known to satisfy a Palais–Smale condition, and so, the technique of Sacks–Uhlenbeck consists in constructing $$\alpha $$ α -harmonic maps for $$\alpha >1$$ α > 1 and then letting $$\alpha \rightarrow 1$$ α → 1 . The extension of this scheme to Dirac-harmonic maps meets with several difficulties, and in this paper, we start attacking those. We first prove the existence of nontrivial perturbed $$\alpha $$ α -Dirac-harmonic maps when the target manifold has nonpositive curvature. The regularity theorem then shows that they are actually smooth if the perturbation function is smooth. By $$\varepsilon $$ ε -regularity and suitable perturbations, we can then show that such a sequence of perturbed $$\alpha $$ α -Dirac-harmonic maps converges to a smooth coupled $$\alpha $$ α -Dirac-harmonic map.

Existence of Generalized Augmented Lagrange Multipliers for Constrained Optimization Problems

The augmented Lagrange multiplier as an important concept in duality theory for optimization problems is extended in this paper to generalized augmented Lagrange multipliers by allowing a nonlinear support for the augmented perturbation function. The existence of generalized augmented Lagrange multipliers is established by perturbation analysis. Meanwhile, the relations among generalized augmented Lagrange multipliers, saddle points, and zero duality gap property are developed.

An application of chaos gray-encoded genetic algorithm for Philip infiltration model

To improve the precision of parameters? estimation in Philip infiltration model, chaos gray-coded genetic algorithm was introduced. The optimization algorithm made it possible to change from the discrete form of time perturbation function to a more flexible continuous form. The software RETC and Hydrus-1D were applied to estimate the soil physical parameters and referenced cumulative infiltration for seven different soils in the USDA soil texture triangle. The comparisons among Philip infiltration model with different numerical calculation methods showed that using optimization technique can increase the Nash and Sutcliffe efficiency from 0.82 to 0.97, and decrease the percent bias from 14% to 2%. The results indicated that using the discrete relationship of time perturbation function in Philip infiltration model?s numerical calculation underestimated model?s parameters, but this problem can be corrected a lot by using optimization algorithm. We acknowledge that in this study the fitting of time perturbation function, Chebyshev polynomial with order 20, did not perform perfectly near saturated and residue water content. So exploring a more appropriate function for representing time perturbation function is valuable in the future.

DIAGNOSA STATUS RESIKO JANTUNG KORONER MENGGUNAKAN METODE FUZZY NON STATIONARY

Penyakit jantung koroner (PJK) merupakan penyakit yang apabila sudah terdiagnosa perlu sekali diawasi karena beresiko tinggi terhadap kematian. Resiko kematian tersebut perlu diminimalisasi dengan membuat sebuah media konsultasi dan monitoring terhadap penderita sesuai gejala yang dialami. Dokter dan paramedis adalah pakar yang berkompeten untuk mediagnosa tingkat resiko penyakit jantung koroner, namun dalam pengambilan keputusan yang sulit terdapat keragaman opini pakar (inter-expert) dan seiring waktu opini pakar pun berubah (intra-expert) karena pengetahuannya terus bertambah berdasarkan adanya gejala baru dari penelitian yang dilakukan, kebiasaan baru, atau dipengaruhi keadaanemosi.Model fuzzy mengatasi permasalahan ketidakpastian. Model fuzzy yang menggunakan himpunan fuzzy non-stationary (FNIS) mereplikasi keragaman pada manusia sehingga mampu mengatasi permasalahan kegaraman opini pada pakar baik inter-expert maupun intra-expert. Sistem yang dibangun menggunakan model fuzzy non-stationary untuk mendiagnosa tingkat resiko jantung koroner berdasarkan 5 input yakni umur, tekanan darah, gula darah, status BMI, dan kolesterol. Fuzzy sistem pada penelitian ini menggunakan mamdani inferensi. Dua fungsi perturbation function yang digunakan sistem adalah fungsi distribusi acak normal pada variabel input dan fungsi sinusoidal pada variabel output untukmeng-generate membership function untuk 5 kali perulangan. Hasil perbandingan diagnosa antara pakar, FIS, dan FNIS didapati bahwa FNIS lebih tepat dibandingkan FIS sesuai diagnosa pakar secara manual.

Eigenvalue, Unilateral Global Bifurcation and Constant Sign Solution for a Fractional Laplace Problem

In this paper, we apply the Ljusternik–Schnirelmann theory to deal with the eigenvalues and eigenfunctions of the fractional Laplace operator. It shows that there exists a simple and isolated principal eigenvalue [Formula: see text] such that under certain conditions on the perturbation function [Formula: see text], [Formula: see text] is a bifurcation point of the problem [Formula: see text] where [Formula: see text], [Formula: see text] is a smooth and bounded domain, [Formula: see text] [Formula: see text] with [Formula: see text] and [Formula: see text] satisfies the Carathéodory condition in the first two variables. There are two distinct unbounded subcontinua [Formula: see text] and [Formula: see text], consisting of the continuum [Formula: see text] emanating from [Formula: see text]. As an application of the unilateral global bifurcation result, we extend our investigation to the existence of constant sign solutions for a class of related nonlinear fractional Laplace problems. Some known results on the fractional Laplace problem in the literature are generalized.

Realistic f(T) model describing the de Sitter epoch of the dark energy dominated universe

We consider an exponential model within the so-called f(T) theory of gravity, where T denotes the torsion scalar. We focus our attention on a cosmological feature of a f(T) model, checking whether it may describe the de Sitter stage of the current universe according to the evolution of the redshift, z. Our results show that the model reproduces the de Sitter stage only for low redshifts, where the perturbation function approached zero, whereas the effective parameter of the equation of state goes to –1, which is the expected behavior for any model able to reproduce the de Sitter stage.

Analysis of Mechanics of Disturbed Materials Based on Theory of Duality Disturbance

Materials exhibit different characteristics in different levels. Apparent behavior and properties of the material are based on actual measurements and they were studied by the traditional theorems and theories. The article studied a new method for material analysis--analysis of mechanics of disturbed materials based on theory of duality disturbance. For material in the any deformed state，a given material element can be treated as mixed state included RND( RND: Relatively Non-Disturbed) and RCD (RCD: Relatively Complete Disturbed). "Duality" state is made of references state of RND and RCD.[1-3] The apparent behavior of disturbing engineering materials use appropriate perturbation function to describe which connect with "duality".

Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality

Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka G., On gap functions for equilibrium problems via Fenchel duality, Pac. J. Optim., 2006, 2(3), 667–678] and [Altangerel L., Boţ R.I., Wanka G., On the construction of gap functions for variational inequalities via conjugate duality, Asia-Pac. J. Oper. Res., 2007, 24(3), 353–371]. By particularizing the perturbation function we rediscover several gap functions from the literature. We also characterize the solutions of various variational inequalities and equilibrium problems by means of the properties of the convex subdifferential. In case no regularity condition is fulfilled, we deliver also necessary and sufficient sequential characterizations for these solutions. Several examples are illustrating the theoretical aspects.

WALL COMPLIANCE EFFECT ON THE FLOW OF COMPRESSIBLE NON-NEWTONIAN FLUID

The peristaltic flow of Jeffrey fluid in a microchannel with compliant wall has been investigated. The rheological effects and compressibility of the fluid are given proper attention. Perturbation approach has been employed when the ratio of the wave amplitude to the radius of the pore is small. Expressions of perturbation function, mean axial velocity distribution, mean velocity at the boundaries and critical values are derived. The variations of various interesting parameters are shown and examined very carefully.