Solutions for certain classes of Riccati differential equation

We derive some analytic closed-form solutions for a class of Riccati equation y'(x)-\lambda_0(x)y(x)\pm y^2(x)=\pm s_0(x), where \lambda_0(x), s_0(x) are C^{\infty}-functions. We show that if \delta_n=\lambda_n s_{n-1}-\lambda_{n-1}s_n=0, where \lambda_{n}= \lambda_{n-1}^\prime+s_{n-1}+\lambda_0\lambda_{n-1} and s_{n}=s_{n-1}^\prime+s_0\lambda_{k-1}, n=1,2,..., then The Riccati equation has a solution given by y(x)=\mp s_{n-1}(x)/\lambda_{n-1}(x). Extension to the generalized Riccati equation y'(x)+P(x)y(x)+Q(x)y^2(x)=R(x) is also investigated.Comment: 10 page

Solvable Systems of Linear Differential Equations

The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear differential equations. The termination criteria of AIM will be re-examined and the whole theory is re-worked in order to fit this new application. As a result of our investigation, an interesting connection between the solution of linear systems and the solution of Riccati equations is established. Further, new classes of exactly solvable systems of linear differential equations with variable coefficients are obtained. The method discussed allow to construct many solvable classes through a simple procedure.Comment: 13 page

Gambaran Status Gizi pada Pasien Penyakit Paru Obstruktif Kronik (Ppok) yang Menjalani Rawat Jalan di RSUD Arifin Achmad Pekanbaru

Chronic Obstructive Pulmonary Disease (COPD) is one of pulmonary disease that becomes health problem in world, including Indonesia. Nutritional status is the condition of health of a person that is influenced by the intake and utilisation of nutrients. COPD may affect the nutritional status and cause malnutrition, otherwise malnutrition may increase risk of complications, morbidity and mortality rate of COPD's patient. Nutritional status and malnutrition also affected the quality of life COPD's patient. This study was using descriptive methods with crossectional approached. The sampling technique used consecutive sampling. The study was held on February-March 2016 with number of sample is 60 patients with COPD in Pulmonary Polyclinic of Arifin Achmad Pekanbaru general hospital. The result of this study is characteristic based age showed 32 (53,3%) persons were >65 years old, 55 (91,7%) persons were male. Characteristic based on occupation showed 33 (55,0%) persons were retired, 48 (80,0%) persons were ex-smoker, 31 (51,7%) persons had COPD for 1-5 years, and 35 (58,3%) persons with good appetite. Nutritonal status based on Body Mass Index (BMI) showed 28 (47,0%) persons had normal category. Nutritional status based on Mid-upper Arm Circumference (MUAC) measurement showed 48 (80,0%) persons had ideal nutrition category. The risk of malnutrition based on Malnutrition Universal Screening Tool (MUST) showed 26 (43,0%) persons were low risk category

Integration of SPT (N-value), mackintosh probe (M-value) and resistivity values for soft soil assessment

2-D resistivity method has been used in association with Mackintosh probe and Standard Penetration Test (SPT) to investigate the ground properties at Universiti Sains Malaysia, Pulau Pinang. The purpose of this study was to determine the resistivity value of the subsurface material together with N-value and M-value of the particular location. The study also aimed to evaluate whether there is any correlation could be made by the parameters measured. Borehole record revealed that two types of soil exist up to 13 m; loose sand and stiff sandy silt. The loose sand recorded N-value of 8 and M-value of 170 having resistivity value of 790 Ohm.m. On the other hand, stiff sandy silt recorded N-value of 9-11, M-value of 135-170 and showing resistivity value of 415-785 Ohm.m. The results showed no clear relation between those geotechnical strength parameters with the resistivity imaging result. It is due to non-existence of distinctive differences in the electrical conductivity of the mentioned ground material when they are in the low strength bracket. However, the resistivity result suggested the presence of higher resistance material that is dry loose sand. The resistivity result was able to detect the water saturated zone near the ground surface, which showed low N-value and M-value

Green's function for a Schroedinger operator and some related summation formulas

Summation formulas are obtained for products of associated Lagurre polynomials by means of the Green's function K for the Hamiltonian H = -{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of a Mercer type theorem that arises in connection with integral equations. The new approach introduced in this paper may be useful for the construction of wider classes of generating function.Comment: 14 page

Cryptographical Properties of Ising Spin Systems

The relation between Ising spin systems and public-key cryptography is investigated using methods of statistical physics. The insight gained from the analysis is used for devising a matrix-based cryptosystem whereby the ciphertext comprises products of the original message bits; these are selected by employing two predetermined randomly-constructed sparse matrices. The ciphertext is decrypted using methods of belief-propagation. The analyzed properties of the suggested cryptosystem show robustness against various attacks and competitive performance to modern cyptographical methods.Comment: 4 pages, 2 figure

Asymptotic iteration method for eigenvalue problems

An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.Comment: 14 page

Typical Performance of Gallager-type Error-Correcting Codes

The performance of Gallager's error-correcting code is investigated via methods of statistical physics. In this approach, the transmitted codeword comprises products of the original message bits selected by two randomly-constructed sparse matrices; the number of non-zero row/column elements in these matrices constitutes a family of codes. We show that Shannon's channel capacity is saturated for many of the codes while slightly lower performance is obtained for others which may be of higher practical relevance. Decoding aspects are considered by employing the TAP approach which is identical to the commonly used belief-propagation-based decoding.Comment: 6 pages, latex, 1 figur