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We consider the fractional relativistic Schr¨odinger-Choquard equation ... where ε > 0 is a small parameter, s ∈ (0, 1), m > 0, N > 2s, μ ∈ (0, 2s), (-Δ + m2)s is the fractional relativistic Schr¨odinger operator, V: RN → R is a continuous potential having a local minimum, f: R → R is a continuous nonlinearity with subcritical growth at infinity and F(t) = t 0 f(τ)dτ. Exploiting appropriate variational arguments, we construct a family of solutions concentrating around the local minimum of V as ε → 0. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the following fractional relativistic Schrödinger equation with critical growth: (−Δ+m2)su+V(εx)u=f(u)+u2s*−1inRN,u∈Hs(RN),u>0inRN,\left\{\begin{array}{ll}{\left(-\Delta +{m}^{2})}^{s}u+V\left(\varepsilon x)u=f\left(u)+{u}^{{2}_{s}^{* }-1}& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N},\\ u\in {H}^{s}\left({{\mathbb{R}}}^{N}),\hspace{1.0em}u\gt 0& \hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N},\end{array}\right. where ε>0\varepsilon \gt 0 is a small parameter, s∈(0,1)s\in \left(0,1), m>0m\gt 0, N>2sN\gt 2s, 2s*=2NN−2s{2}_{s}^{* }=\frac{2N}{N-2s} is the fractional critical exponent, (−Δ+m2)s{\left(-\Delta +{m}^{2})}^{s} is the fractional relativistic Schrödinger operator, V:RN→RV:{{\mathbb{R}}}^{N}\to {\mathbb{R}} is a continuous potential, and f:R→Rf:{\mathbb{R}}\to {\mathbb{R}} is a superlinear continuous nonlinearity with subcritical growth at infinity. Under suitable assumptions on the potential VV, we construct a family of positive solutions uε∈Hs(RN){u}_{\varepsilon }\in {H}^{s}\left({{\mathbb{R}}}^{N}), with exponential decay, which concentrates around a local minimum of VV as ε→0\varepsilon \to 0.

Fuzzy singular Lyapunov matrix equations have many applications, but feasible numerical methods to solve them are absent. In this paper, we propose an efficient numerical method for fuzzy singular Lyapunov matrix equations, where A is crisp and semi-stable. In our method, we transform fuzzy singular Lyapunov matrix equation into two crisp Lyapunov matrix equations. Then we solve the least squares solutions of the two crisp Lyapunov matrix equations, respectively. The existence of fuzzy solution is also considered. At last, two small examples are presented to illustrate the validate of the method and two large scale examples that the existing method fails to slove are presented to show the efficiency of the method. [ABSTRACT FROM AUTHOR]

The aim of this study is to recognize obstacles to using extension methods from the perspective of agricultural employees. The suryey was conducted on the society of all 180 employees in agricultural extension units in Nineveh governorate and the final research sample was of 90 employees which represent 50% of society. A research tool consisting of two sections was created to fulfil the objective and gather data for this study. The first part is concerned with some personal variables (age, certificate, years in service in agricultural divisions, specialization, participation in extension activities, and desire to work in extension of employees. The second included a number of items (25 questions) about obstacles to using extension methods from employees perspective. Results showed that the level of obstacles of using extension method in general, is moderate, according to employees perspective. There is a significant correlation between obstacles to using extension methods and independent variables (age, years of service in guidance). The researcher concludes that the former variables affect to recognizing obstacles to using extension methods from employees' perspectives. Results also show an absence of correlation between obstacles to using the extension method and the variables (academic achievement, specialization, participation in agricultural extension activities, and desire to work in extension). It is concluded that these variables do not play part in recognizing obstacles to using extension methods from the agricultural employee perspective. [ABSTRACT FROM AUTHOR]

This paper is concerned with the following sublinear fractional Schrödinger equation: (− Δ) s u + V (x) u = a (x) | u | q − 1 u + f (x) , x ∈ R N , where s ∈ (0 , 1) , q ∈ ((1 / 2 s ∗ − 1) , 1) , N>2s, 2 s ∗ = 2 N / (N − 2 s) , (− Δ) s is the fractional Laplacian operator, and V, a both change sign in R N , f ≠ 0 is a nonnegative perturbation such that f ∈ L (q + 1) / q (R N) ∩ L 2 s ∗ / (2 s ∗ − 1) (R N). By using the s-harmonic extension technique and suitable variational methods, we prove the existence of at least two nontrivial solutions for the problem. [ABSTRACT FROM AUTHOR]

In this paper, we study coupled wave equations which are defined on a semi‐infinite interval and a finite interval, respectively, and obtain their d'Alembert type traveling wave solutions with finite closed forms. We also illustrate the results by concrete examples. These results generalized the corresponding ones for single wave equation wherein the solution is usually expressed by Fourier series. [ABSTRACT FROM AUTHOR]

In this paper we study the following class of fractional relativistic Schrödinger equations: { (−Δ + m2)su + V (ε x)u = ƒ(u) in RN, u ∈ Hs(RN), u > 0 in RN where ε > 0 is a small parameter, s ∈ (0,1), m > 0, N > 2s, (−Δ + m2)s is the fractional relativistic Schrödinger operator, V : RN → R is a continuous potential satisfying a local condition, and ƒ : R &#8594: R is a continuous subcritical nonlinearity. By using a variant of the extension method and a penalization technique, we first prove that, for ε > 0 small enough, the above problem admits a weak solution which concentrates around a local minimum point of V as ε → 0. We also show that uε has an exponential decay at infinity by constructing a suitable comparison function and by performing some refined estimates. Secondly, by combining the generalized Nehari manifold method and Ljusternik-Schnirelman theory, we relate the number of positive solutions with the topology of the set where the potential V attains its minimum value. [ABSTRACT FROM AUTHOR]

Agriculture extension is an effort to change the farmers’ behaviors as well as their families in order to solve their problems in farming, so that they will be able to increase production and their welfares. Success in Agriculture extension process is determined by appropriate method and media application. Objectives of the research were to study the extent of method and media application in extension and to formulate strategy of method and media application in extension on the Farmer Group of Harapan Sejahtera at the Subdistrict of East Tarakan. Respondents of the research were members Group of Women Farmers of Harapan Sejahtera, 23 women and 2 Informants of Agriculture extension agents. Data analysis used Likert’s scale and SWOT analysis. Results of the research showed that the extent of extension media and method application on the Farmer Group of Harapan Sejahtera are in medium categories, which have scores 11 and 12, respectively. Strategies of the application of method and media on extension toward the Farmer Group of Harapan Sejahtera include; (1) implementation of group method in giving the extension, (2) establishing the Meeting Hall as supporting means to perform extension activities, (3) utilizing online media (cyber extension) to transfer the extension.

In view of problems that traditional multi-objective predictive control method based on weighting method cannot effectively deal with contradiction of objectives and complex design of weight coefficient, a multi-objective optimization predictive control method of high-power explosion-proof permanent magnet motor based on two-layer structure compatible framework was proposed. The d-axis current tracking, q-axis current tracking and midpoint potential balance were divided into compatible optimization layers. By introducing boundary interval, compatible control of the three objectives was effectively realized. Switching loss was divided into optimal optimization layer. A switching frequency measurement method based on extension method was proposed. By approximately measuring switching time of multiple control cycles, average switching frequency of the system was effectively reduced. The simulation results show that the proposed method can achieve compatible control of current command tracking and midpoint potential, and can effectively reduce average switching frequency of the system.

In this paper, we investigate the existence of multiple solutions for the following two fractional problems:

In this paper, we are interested in the stabilization of the flow modeled by the Saint-Venant equations. We have solved two problems in this study. The first, we have proved that the operator associated to the Saint-Venant system has a finite number of unstable eigenvalues. Consequently, the system is not exponentially stable on the space L 2 (Ω) × L 2 (Ω) , but is exponentially stable on a subspace of the space L 2 (Ω) × L 2 (Ω) , (Ω is a given domain). The second problem, if the advection is dominant, the natural stabilization is very slow. To solve these problems, we have used an extension method due to Russel (1974) and Fursikov (2002). Thanks to this method, we have determined a boundary Dirichlet control able to accelerate the stabilization of the flow. Also, the boundary Dirichlet control is able to kill all the unstable eigenvalues to get an exponentially stable solution on the space L 2 (Ω) × L 2 (Ω). Then, we extend this method to the finite difference equations analog of the continuous Saint-Venant equations. Also, in this case, we obtained similar results of stabilization. A finite difference scheme is used to compute the control and several numerical experiments are performed to illustrate the efficiency of the control. [ABSTRACT FROM AUTHOR]

Topological conjugacy between multifunctions plays an important role in the research of dynamical systems. This paper deals with conjugacies of strictly increasing and upper semicontinuous multifunctions on a closed interval with finite set-valued points. All conjugacies between these two multifunctions are constructed with an extension method. The C 1 smoothness of the conjugacies is also given. Moreover, an example is presented to illustrate the applications of the main results. [ABSTRACT FROM AUTHOR]

An electrocardiogram (ECG) documents the voltage changes during heartbeats. It captures electrocardiographic signals in a noninvasive way. ECGs are complicated and vary from person to person, making them ideal for use in biometric recognition systems. A number of studies have shown that ECG signals are nonlinear curves and dynamically chaotic. The ECG signals were measured on the basis of the Einthoven's triangle principle in this study. Combining captured ECG signals using ECG biosensors and a data acquisition (DAQ) card, LabVIEW was used to design a human-machine interface (HMI) to display the processed ECG signals for test subjects. The saved ECG data were plotted in a dynamical map of the chaotic dynamic error using a master-slave chaotic system. The chaotic eye was selected as a feature and an identity database was built using an element model. Personal identity was identified by categorizing with an extension method. Thirty-six subjects were tested and the identification accuracy was 94.4%. The MIT-BIH Normal Sinus Rhythm Database (NSRDB) and an arrhythmia database were used in this study. Using the extension method, the classification accuracy between normal and cardiac arrhythmia was 91.67%, and the accuracy was increased to 100% when matter element extensibility was employed. Results suggested that the biometric recognition method developed in this study performs identification rapidly with high positive recognition rate and reliability. [ABSTRACT FROM AUTHOR]

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Using the extension method, we study the one-parameter symmetry groups of the heat equation ∂tp = Δp, where Δ = X 1 2 + X 2 2 is the sub-Laplacian constructed by a Goursat distribution span({X1, X2}) in ℝn, where the vector fields X1 and X2 satisfy the commutation relations [X1, Xj] = Xj+1 (where Xn+1 = 0) and [Xj, Xk] = 0 for j ≥ 1 and k ≥ 1. We show that there are no such groups for n ≥ 4 (with exception of the linear transformations of solutions which are admitted by every linear equation). [ABSTRACT FROM AUTHOR]

A study was conducted in Krishnagiri district of Tamil Nadu state to understand the utilization pattern of extension tools and methods by the agricultural extension agents. As ICT revolution is slowly conquering the rural sector, it becomes imperative that the agricultural extension agents transform themselves to the changing times and develop competencies in utilizing these ICTs. The study explored the usage of various extension tools and methods by the change agents and the constraints faced in utilizing them. The findings revealed that the extension functionaries frequently used the individual contact methods viz., telephone, office calls and farm and home visits in the process of transfer of technology. Least efforts were shown in sending SMS based communication. Meetings were the common and frequently adopted group contact method. Demonstrations, farmer field school, farmer’s interest groups, field trips and farmer training programmes were moderately adopted. Posters, leaflets and pre-season campaigns were the widely adopted mass contact methods. They possess least skill in utilizing farm magazines, presenting television and radio programmes, which are among the most popular and most efficient mass contact methods. The extension functionaries need to be trained adequately on the wider use of electronic communication methods like e mails, and SMS in the local language. Efforts should be taken up to sensitize the importance and train the extension agents in the usage of different group and mass contact methods.

Abstrak: Pemahaman mendalam terkait proses interaksi dan komunikasi yang terjadi dalam suatu struktur sosial petani, memudahkan pelaksanaan penyuluhan yang efektif dan efisien baik dari segi waktu maupun tenaga. Tujuan dari pengkajian ini adalah mengidentifikasi dan merumuskan pola jaringan sosial yang ada di masyarakat petani untuk komoditas padi spesifik kabupaten/etnis, mengetahui faktor-faktor yang mempengaruhi dalam percepatan transfer teknologi padi di dalam jaringan sosial petani, mengidentifikasi media dan metode penyuluhan yang relatif paling disenangi oleh pengguna dalam jaringan sosial dan merumuskan strategi penyuluhan PTT Padi. Pengkajian dilaksanakan di 3 kabupaten di Jawa Timur yang mewakili sosial budaya/etnis. Metode yang digunakan dalam pengkajian ini adalah dengan pendekatan sosiometri. Populasi dan sampel yang menjadi objek kajian merupakan pihak/pelaku yang terdedah oleh informasi PTT Padi Sawah. Hasil analisis menunjukkan bahwa hand phone (HP) dan alat transportasi (motor/sepeda) merupakan sarana komunikasi yang diperlukan untuk mempererat dan mempercepat komunikasi dalam jaringan komunitas. Upaya yang sering dilakukan, agar inovasi teknologi cepat sampai pada anggota jaringan, adalah melakukan pertemuan tatap muka dan kunjungan, media penyuluhan yang paling disukai anggota jaringan komunitas untuk transfer inovasi teknologi adalah media televise, serta brosur/buku saku dan metode penyuluhan yang dinilai paling efektif adalah sekolah lapang, temu lapang dan demplot. Pola Jaringan Komunikasi di Kabupaten Tuban, pola interaksi yang terbentuk cenderung terdispersi pada jalur interaksi yang relatif panjang. Untuk Pola jaringan komunikasi hasil pengkajian di Kabupaten Trenggalek menunjukkan bahwa pola komunikasi antar individu petani bersifat lebih teratur, sedangkan pola jaringan komunikasi di Kabupaten Jember, bahwa struktur komunikasinya menunjukkan multi saluran. Hal ini ditandai dimana dari tiga level tersebut interaksi timbal balik dapat terjadi tanpa menganut siapa yang menjadi tokoh sentralnya. Abstract: In-depth understanding related to the interaction and communication process that occurs in a social structure of farmers facilitates the implementation of effective and efficient counseling both in terms of time and energy. The purpose of this study is to identify and formulate the existing social network patterns in farmer communities for district / ethnic-specific rice commodities, to know the factors that influence the acceleration of rice technology transfer in farmers' social networks, identify the media and the most favored extension methods by users in social networks and formulating rice PTT extension strategies. The assessment was carried out in 3 districts in East Java that represented social culture/ethnicity. The method used in this study is a sociometric approach. The population and sample that are the object of study are the parties/actors who are exposed to the information on PTT Paddy Fields. The results of the analysis show that handphones (mobile phones) and transportation equipment (motorbikes/bicycles) are the means of communication needed to strengthen and accelerate communication in the community network. Efforts that are often made, so that technological innovation will quickly reach network members, are conducting face-to-face meetings and visits, the most popular counseling media for community network members to transfer technological innovations is television media, as well as brochures/pocketbooks and extension methods that are considered the most effective, is a field school, field meeting, and demonstration plot. Communication Network Patterns in Tuban Regency, the interaction patterns formed tend to be dispersed on relatively long interaction pathways. The pattern of the communication network as a result of the assessment in Trenggalek Regency shows that the communication pattern between individual farmers is more regular, while the communication network pattern in Jember Regency shows that the communication structure shows multiple channels. This is marked wherefrom these three levels reciprocal interaction can occur without adhering to who is the central figure.