Eigenvalue optimization and its applications in buckling and vibration

Eigenvalue problems are of immense interest and play a pivotal role not only in many fields of engineering but also in pure and applied mathematics. An in-depth understanding of this class of problems is a pre-requisite for vibration and buckling analyses of structures. Design optimization of structures to prevent failure due to instability (bucking) and vibration introduces the problem of determining optimal physical parameters such that load carrying capacity or the fundamental natural frequency is maximized. A classical example of such problems is the Lagrange problem of determining the shape of the strongest column against buckling. The primary objective of this research is to develop discrete models for column buckling and to solve the problem of finding the strongest column by applying fundamental principles of optimization. The physical parameters of optimal discrete link-spring models, which maximize the buckling loads, are reconstructed. It is shown that the optimal system can be determined recursively by using a one parameter iterative loop. The mathematical problem of determining parameters of an affine sum such that the system has extremum eigenvalues was derived and solved. Numerical techniques were developed to aid in the optimization process and were utilized to optimize mass-spring systems. The more complicated problem of finding the shape of the strongest column was also defined as an affine sum by applying finite difference schemes to both the second and fourth order governing differential equations. Optimization techniques and numerical methods were developed to arrive at the shape of the strongest clamped-free and pinned-pinned column. Unimodal solutions of the Lagrange problem were also obtained for the special case where minimum area constraints were given. A mathematical model for columns on elastic foundation also was derived and transformed to an affine sum problem. Unimodal solution of shape of the strongest pinned-pinned column on an elastic foundation was obtained. In addition the application in vibration and buckling, it is believed that the optimization principles and numerical methods developed in this research will be applicable in other fields such as optimal control

Nabla fractional boundary value problem with a non-local boundary condition

In this work, we deal with the following two-point boundary value problem for a finite fractional nabla difference equation with non-local boundary condition: (−(∇ξρ(e) u(z) = p(z, u(z)), z ∈ Nfe+2, u(e) = g(u), u(f) = 0. Here e, f ∈ R, with f −e ∈ N3, 1 < ξ < 2, p : Nfe+2 ×R → R is a continuous function, the functional g ∈ C[Nfe → R] and ∇ξρ(e) denotes the ξth- order Riemann–Liouville backward (nabla) difference operator. First, we derive the associated Green’s function and some of its properties. Using the Guo–Krasnoselskii fixed point theorem on a suitable cone and under appropriate conditions on the non-linear part of the difference equation, we establish sufficient conditions for the existence of at least one positive solution to the boundary value problem. Next, we discuss the uniqueness of the solution to the considered problem. For this purpose, we use Brouwer and Banach fixed point theorem respectively. Finally, we provide an example to illustrate the applicability of established results.Publisher's Versio

Study of insulin levels in hypothyroidism patients

Background: Overt hypothyroidism is an established risk factor for insulin resistance. In this study we find out whether this association exists between insulin resistance and subclinical hypothyroidism. Methods: Serum Insulin, Fasting blood sugar, Cholesterol were estimated in 60 clinically diagnosed patients of hypothyroidism these patients were divided in to two groups as group I, 30 overt hypothyroidism and group II, 30 subclinical hypothyroidism. Results were compared with a group of 30 normal subjects.To measure the level of insulin resistance using HOMA IR software. Results: In our study total cholesterol were significantly high in both overt hypothyroidism and sub clinical hypothyroidism as compared to euthyroid control group and serum TSH and serum insulin levels were positively correlated with total cholesterol levels in hypothyroidism patients. We also found that TSH levels were positively correlated with insulin and HOMA IR in patients with subclinical hypothyroidism. Conclusions: Hence it will be good practice to screen people for presence of subclinical hypothyroidism and insulin resistance for early detection and prolong the appearance of various fatal complications associated with insulin resistance in hypothyroidism.

ESDA2008-59289 DISCRETE MODEL ANALYSIS OF OPTIMAL COLUMNS

ABSTRACT Keller has determined in [2] the shape of the strongest hingedhinged column. This was the stepping stone in the solution of the long standing Lagrange problem of finding the shape of the strongest column in the clamped-free configuration. We consider here the discrete link-spring model of column which is hinged on one side and spring supported on the other side that maximizes the buckling load. It is shown that for certain rigidity of the supporting spring the solution is not unique. For the other range of rigidity the shape of the strongest column is invariant of the spring constant

Isolation of ckit-positive cardiosphere-forming cells from human atrial biopsy

There is increasing interest in developing cell-based therapies to regenerate functional muscle and blood vessels in infarcted dysfunctional myocardium, using stem cells resident in the adult heart. The objective of our study was to identify an easy and cost-effective method for the isolation and expansion of human adult cardiac-resident stem cells. The cells were isolated from right atrial biopsy samples obtained from patients with ischemic heart disease, who were undergoing coronary artery bypass grafting. Two different isolation methods, enzymatic and nonenzymatic, were employed. The cell yield and cluster formation were not significantly different with either of the techniques used for cell isolation. The nonenzymatic method is recommended because of its simplicity and lower cost compared to the enzymatic method

Penning Spectroscopy and Structure of Acetylene Oligomers in He Nanodroplets

Embedded atoms or molecules in a photoexcited He nanodroplet are well-known to be ionized through inter-atomic relaxation in a Penning process. In this work, we investigate the Penning ionization of acetylene oligomers occurring from the photoexcitation bands of He nanodroplets. In close analogy to conventional Penning electron spectroscopy by thermal atomic collisions, the n = 2 photoexcitation band plays the role of the metastable atomic $1s2s$ $^{3,1}S$ He$^\ast$. This facilitates electron spectroscopy of acetylene aggregates in the sub-kelvin He environment, providing the following insight into their structure: The molecules in the dopant cluster are loosely bound van der Waals complexes rather than forming covalent compounds. In addition, this work reveals a Penning process stemming from the n = 4 band where charge-transfer from autoionized He in the droplets is known to be the dominant relaxation channel. This allows for excited states of the remnant dopant oligomer Penning-ions to be studied. Hence, we demonstrate Penning ionization electron spectroscopy of doped droplets as an effective technique for investigating dopant oligomers which are easily formed by attachment to the host cluster.Comment: 22 pages, 1 png figure, 4 postscript figure

Coincident angle-resolved state-selective photoelectron spectroscopy of acetylene molecules: a candidate system for time-resolved dynamics

The acetylene-vinylidene system serves as a benchmark for investigations of ultrafast dynamical processes where the coupling of the electronic and nuclear degrees of freedom provides a fertile playground to explore the femto- and sub-femto-second physics with coherent extreme-ultraviolet (EUV) photon sources both on the table-top as well as free-electron lasers. We focus on detailed investigations of this molecular system in the photon energy range $19...40$ eV where EUV pulses can probe the dynamics effectively. We employ photoelectron-photoion coincidence (PEPICO) spectroscopy to uncover hitherto unrevealed aspects of this system. In this work, the role of excited states of the $C_{2}H_{2}^{+}$ cation, the primary photoion, is specifically addressed. From photoelectron energy spectra and angular distributions, the nature of the dissociation and isomerization channels is discerned. Exploiting the $4\pi$-collection geometry of velocity map imaging spectrometer, we not only probe pathways where the efficiency of photoionization is inherently high but also perform PEPICO spectroscopy on relatively weak channels.Comment: 12 pages, 7 figures, 5 table

Targeting Glioma Stem Cells by Functional Inhibition of a Prosurvival OncomiR-138 in Malignant Gliomas

SummaryMalignant gliomas are the most aggressive forms of brain tumors, associated with high rates of morbidity and mortality. Recurrence and tumorigenesis are attributed to a subpopulation of tumor-initiating glioma stem cells (GSCs) that are intrinsically resistant to therapy. Initiation and progression of gliomas have been linked to alterations in microRNA expression. Here, we report the identification of microRNA-138 (miR-138) as a molecular signature of GSCs and demonstrate a vital role for miR-138 in promoting growth and survival of bona fide tumor-initiating cells with self-renewal potential. Sequence-specific functional inhibition of miR-138 prevents tumorsphere formation in vitro and impedes tumorigenesis in vivo. We delineate the components of the miR-138 regulatory network by loss-of-function analysis to identify specific regulators of apoptosis. Finally, the higher expression of miR-138 in GSCs compared to non-neoplastic tissue and association with tumor recurrence and survival highlights the clinical significance of miR-138 as a prognostic biomarker and a therapeutic target for treatment of malignant gliomas

Effect of quantum confinement on exciton-phonon interactions

We investigate the homogeneous linewidth of localized type-I excitons in type-II GaAs/AlAs superlattices. These localizing centers represent the intermediate case between quasi-two-dimensional (Q2D) and quasi-zero-dimensional localizations. The temperature dependence of the homogeneous linewidth is obtained with high precision from micro-photoluminescence spectra. We confirm the reduced interaction of the excitons with their environment with decreasing dimensionality except for the coupling to LO-phonons. The low-temperature limit for the linewidth of these localized excitons is five times smaller than that of Q2D excitons. The coefficient of exciton-acoustic-phonon interaction is 5 ~ 6 times smaller than that of Q2D excitons. An enhancement of the average exciton-LO-phonon interaction by localization is found in our sample. But this interaction is very sensitive to the detailed structure of the localizing centers.Comment: 6 pages, 4 figure