Design sensitivity analysis of nonlinear structural response

A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use

Strong inapproximability of the shortest reset word

The \v{C}ern\'y conjecture states that every $n$-state synchronizing automaton has a reset word of length at most $(n-1)^2$. We study the hardness of finding short reset words. It is known that the exact version of the problem, i.e., finding the shortest reset word, is NP-hard and coNP-hard, and complete for the DP class, and that approximating the length of the shortest reset word within a factor of $O(\log n)$ is NP-hard [Gerbush and Heeringa, CIAA'10], even for the binary alphabet [Berlinkov, DLT'13]. We significantly improve on these results by showing that, for every $\epsilon>0$, it is NP-hard to approximate the length of the shortest reset word within a factor of $n^{1-\epsilon}$. This is essentially tight since a simple $O(n)$-approximation algorithm exists.Comment: extended abstract to appear in MFCS 201

On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and $1/2+\epsilon$. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-$m$ approximation-resistant OCSPs accepting only a fraction $1 / (m/2)!$ of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P $\neq$ \NP

Accurate determination of electric-dipole matrix elements in K and Rb from Stark shift measurements

Stark shifts of potassium and rubidium D1 lines have been measured with high precision by Miller et al [1]. In this work, we combine these measurements with our all-order calculations to determine the values of the electric-dipole matrix elements for the 4p_j-3d_j' transitions in K and for the 5p_j-4d_j' transitions in Rb to high precision. The 4p_1/2-3d_3/2 and 5p_1/2-4d_3/2 transitions contribute on the order of 90% to the respective polarizabilities of the np_1/2 states in K and Rb, and the remaining 10% can be accurately calculated using the relativistic all-order method. Therefore, the combination of the experimental data and theoretical calculations allows us to determine the np-(n-1)d matrix elements and their uncertainties. We compare these values with our all-order calculations of the np-(n-1)d matrix elements in K and Rb for a benchmark test of the accuracy of the all-order method for transitions involving nd states. Such matrix elements are of special interest for many applications, such as determination of magic wavelengths in alkali-metal atoms for state-insensitive cooling and trapping and determination of blackbody radiation shifts in optical frequency standards with ions.Comment: 5 page

Phytochemical investigation of seeds of Trachyspermum ammi Linn. by GC-MS

The present study embraces phytochemical investigation of the essential oil extracted from the mature seeds of Trachyspermum ammi Linn for different constituents by subjecting the oil to gas chromatography-mass spectrometry (GC-MS) analysis. The identification of the constituents is based upon retention indices and by comparison of their mass spectral fragmentation patterns against the commercial library mass spectra (Wiley, Nist etc.). Ellagic acid (EA), which is a natural phenol antioxidant, has been isolated from methanol extract from the mature seeds of Trachyspermum ammi Linn. Also, Thymol (Thl), a naturally occurring phenolic compound, has been crystallized by the reported standard procedure from oil extracted from these mature seeds. Both these compounds have been evaluated for their possible anti-cancer effect against a selected panel of human cancer cell lines by means of sulforhodamine B assay

Phytochemical Study of Nothapodytes foetida by LC-ESI-MS

In the present study, hyphenated technique using dyad system of high performance liquid chromatography with diode array detection directly coupled with electrospray ionization mass spectrometry (LC-ESI-MS) has been employed for identification of camptothecines and some minor constituents of methanol extract from different parts of Nothapodytes foetida on the basis of systematic mass spectrum analysis without isolation and purification of these components. Also, a simple, precise, sensitive and reproducible LC-MS method has been developed for quantification of camptothecin (CPT), a potent cytotoxic isoquinoline alkaloid, in methanol extract from these different parts of Nothapodytes foetida using the same technique

Recovery Ventilation and Oxygen Debt-A Mathematical Model for the Prediction of Recovery Ventilation

A Mathematical model has been evolved for the estimation of recovery ventilation following an exercise. The model has been used to estimate recovery ventilation in moderate to heavy exercise for a period of 32 minutes. The model gives satisfactory predictions for persons of different age groups and under different environment conditions thus establishing its universal applicability