The paper is concerned with the state and proof of the solvability theorem of unique state vector solution (SVS) of triple nonlinear hyperbolic boundary value problem (TNLHBVP), via utilizing the Galerkin method (GAM) with the Aubin theorem (AUTH), when the boundary control vector (BCV) is known. Solvability theorem of a boundary optimal control vector (BOCV) with equality and inequality state vector constraints (EINESVC) is proved. We studied the solvability theorem of a unique solution for the adjoint triple boundary value problem (ATHBVP) associated with TNLHBVP. The directional derivation (DRD) of the "Hamiltonian"(DRDH) is deduced. Finally, the necessary theorem (necessary conditions "NCOs") and the sufficient theorem (sufficient conditions" SCOs"), together denoted as NSCOs, for the optimality (OP) of the state constrained problem (SCP) are stated and proved.
Solutions of dyes Rhodamine 6G (Rh6G) and Coumarin480(C480) were prepared at five concentrations (1x10-3, 5x10-4, 1x10-4, 5x10-5 and1x10-5) mol/l, the mixing was stirred to obtain on a homogenous solution, the(poly methyl-methacrylate) (PMMA) was solved by chloroform solvent with certain ratio, afterward (PMMA+Rh6G) and (PMMA+C480) thin films were prepared by casting method on glass block which has substrate with dimensions (7.5 x2.5)cm2, the prepared samples were left in dark place at room temperature for 24 hours to obtain uniform and homogenous thin films. UV-VIS absorption spectra, transmission spectra and fluorescence spectra were done to measure linear refractive index and linear absorption coefficient. The nonlinear optical proper
... Show MoreA huge potential from researchers was presented for enhancing the nonlinear optical response for materials that interacts by light. In this work, we study the nonlinear optical response for chemically prepared nano- fluid of silver nanoparticles in de-ionized water with TSC (Tri-sodium citrate) protecting agent. By the means of self-defocusing technique and under CW 473 nm blue laser, the reflected diffraction pattern were observed and recorded by CCD camera. The results demonstrate that, the Ag nano-fluid shows a good third order nonlinear response and the magnitude of the nonlinear refractive index was in the order of 10−7 cm2/W. We determine the maximum change of the nonlinear refractive index and the related phase shift for the mat
... Show MoreActive vibration control is the main problem in different structure. Smart material like piezoelectric make a structure smart, adaptive and self-controlling so, they are effective in active vibration control. In this paper piezoelectric elements are used as sensors and actuators in flexible structures for sensing and actuating purposes, and to control the vibration of a cantilever beam by using sliding mode control. The sliding mode controller (SMC) is designed to attenuate the vibration induced by initial tip displacement which is equal to 15 mm. It is designed based on the balance realization reduction method where three states are selected for the reduced model from the 24th states that describe the c
... Show MoreA partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.
Thirty local fungal isolates according to Aspergillus niger were screened for Inulinase production on synthetic solid medium depending on inulin hydrolysis appear as clear zone around fungal colony. Semi-quantitative screening was performed to select the most efficient isolate for inulinase production. the most efficient isolate was AN20. The optimum condition for enzyme production from A. niger isolate was determined by busing a medium composed of sugar cane moisten with corn steep liquor 5;5 (v/w) at initial pH 5.0 for 96 hours at 30 0C . Enzyme productivity was tested for each of the yeast Kluyveromyces marxianus, the fungus A. niger AN20 and for a mixed culture of A. niger and K. marxianus. The productivity of A. niger gave the highest
... Show MoreThis paper presents designing an adaptive state feedback controller (ASFC) for a magnetic levitation system (MLS), which is an unstable system and has high nonlinearity and represents a challenging control problem. First, a nonadaptive state feedback controller (SFC) is designed by linearization about a selected equilibrium point and designing a SFC by pole-placement method to achieve maximum overshoot of 1.5% and settling time of 1s (5% criterion). When the operating point changes, the designed controller can no longer achieve the design specifications, since it is designed based on a linearization about a different operating point. This gives rise to utilizing the adaptive control scheme to parameterize the state feedback controll
... Show MoreThe aim of this work is to study the correlation between the electrons for Li atom in ground state through the calculation of the inter-particle distribution function f (r12) and inter-particle expectation values . By using the f(r12) function for KL shell in both singlet and triplet state .The Fermi hole have been evaluated .In this work the Hartree-Fock wave function (1993) have been used.
Verbs are an important material in the construction of the sentence, as they are among the requirements of every sophisticated language, and in this regard, Ibn Al-Gothic (d. 367 AH): “Know that verbs are the origins of the buildings of most speech, and thus scholars called them buildings.” Verbs are the source of expression of the speakers’ ideas to represent the element of activity and movement, and with their knowledge We infer the meanings of Arabic words, and Ibn Al-Sarraj (d. 316 AH) defined it: “The verb denotes a meaning and a time, and that time is either past, present, or future.” Its letters are original and does not drop from its construction a letter in the conjugation of its conjugations, and it is in Arabic two type
... Show More