BMO and Elasticity: Korn’s Inequality; Local Uniqueness in Tension

In this manuscript two BMO estimates are obtained, one for Linear Elasticity and one for Nonlinear Elasticity. It is first shown that the BMO-seminorm of the gradient of a vector-valued mapping is bounded above by a constant times the BMO-seminorm of the symmetric part of its gradient, that is, a Korn inequality in BMO. The uniqueness of equilibrium for a finite deformation whose principal stresses are everywhere nonnegative is then considered. It is shown that when the second variation of the energy, when considered as a function of the strain, is uniformly positive definite at such an equilibrium solution, then there is a BMO-neighborhood in strain space where there are no other equilibrium solutions.

Control for the Space Tether System Motion

This paper proposed a study of a spatial tether system (STS), composed by two satellite (a main satellite and a subsatellite), with the objective of developing a control system in which the motion of the subsatellite is limited in the orbital plane of the main satellite. The linear quadratic regulator (LQR) method is used to implement this control, which is an optimal control with state feedback to predict the linearization of the equations of motion to calculate the feedback gain, using the resolution of Riccati equation. The results show an effective control, with the motion of the subsatellite limited only to the stretch of the cable that links both satellites. However, it is necessary to introduce an auxiliary torque, since the linearized equation associated with the second variation of the angle out of the plan does not have a term independent of the state vector.

Variational formulations of steady rotational equatorial waves

When the vorticity is monotone with depth, we present a variational formulation for steady periodic water waves of the equatorial flow in the f-plane approximation, and show that the governing equations for this motion can be obtained by studying variations of a suitable energy functional 𝓗 in terms of the stream function and the thermocline. We also compute the second variation of the constrained energy functional, which is related to the linear stability of steady water waves.

Stable s-minimal cones in ℝ3 are flat for s ~ 1

We prove that half spaces are the only stable nonlocal s-minimal cones in {\mathbb{R}^{3}}, for {s\in(0,1)} sufficiently close to 1. This is the first classification result of stable s-minimal cones in dimension higher than two. Its proof cannot rely on a compactness argument perturbing from {s=1}. In fact, our proof gives a quantifiable value for the required closeness of s to 1. We use the geometric formula for the second variation of the fractional s-perimeter, which involves a squared nonlocal second fundamental form, as well as the recent BV estimates for stable nonlocal minimal sets.

The Jacobi morphism and the Hessian in higher order field theory; with applications to a Yang–Mills theory on a Minkowskian background

We characterize the second variation of an higher order Lagrangian by a Jacobi morphism and by currents strictly related to the geometric structure of the variational problem. We discuss the relation between the Jacobi morphism and the Hessian at an arbitrary order. Furthermore, we prove that a pair of Jacobi fields always generates a (weakly) conserved current. An explicit example is provided for a Yang–Mills theory on a Minkowskian background.

Analysis of Strength of Concrete with Partial Replacement of Cement with Fly Ash and Fine Aggregate with Blast Furnance Slag Sand

The utilization of waste materials from the industries has been continuously gaining emphasis in the construction work recently. The present work is to use Processed Granulated Blast Furnace Slag Sand and Fly ash as combined replacement for river sand and ordinary Portland cement respectively. M35 grade of concrete with W/C 0.4 will be adopted with two percentages of cement replacement by Fly Ash i.e, 30% and 40%, along with this the slag sand is varied from 0% to 100% in step of 20%. In first variation, 30% Fly Ash is replaced by cement and slag sand is varied as 0%, 20%, 40%, 60%, 80% and 100%. In second variation, 40% GGBS is replaced with cement and slag sand is varied as 0%, 20%, 40%, 60%, 80%, and 100%. For all mixes compressive strength, split tensile and flexural strength will be determined at different days of curing. The strength of cube specimens, cylinders and beams will be determined and compared with conventional concrete specimens. The beams are tested for flexure, under two point loading condition. Different parameters will be investigated in detail. In this paper literature is reviewed in detail to understand the experimental analysis.

Regularity and Conjugacy for Constrained Variational Problems

For problems in the calculus of variations involving equality and inequality mixed constraints we characterize, in terms of an extended notion of conjugate points, the sign of a quadratic form which corresponds to the second variation of the integral to be minimized. Second order necessary conditions are then derived assuming the well-known constraint qualification of regularity in the sense that, with respect to the set of mixed constraints, both the tangent cone and the set of tangential constraints coincide.

AKTIVITAS ANTIOKSIDAN BLACK GARLIC DENGAN VARIASI JENIS BAWANG (Allium sp) DAN LAMA PEMERAMAN

Black garlic adalah produk fermentasi dari bawang putih yang dipanaskan dengan suhu antara 65 – 80ºC dan kelembapan 70 – 80% dari suhu kamar selama satu bulan. Black garlic telah diketahui memiliki kandungan antioksidan yang cukup tinggi sehingga bisa menjadi produk baru dari jenis bawang putih yang berfungsi menghambat radikal bebas dalam tubuh. Menentukan jenis bawang yang menghasilkan aktivitas antioksidan lebih tinggi setelah melalui proes pemanasan black garlic. Penelitian ini menggunakan metode rancangan acak lengkap 2 faktorial, dengan faktor pertama adalah waktu perlakuan pemanasan dengan suhu 65-850C, selama 8 hari, 12 hari, 16 hari dan faktor kedua variasi jenis bawang, bawang garlic, bawang kating, bawang lanang. Analisis kimia yaitu aktivitas antioksidan, kadar air, total fenol, gula total dan uji sensoris yaitu tekstur lembut, rasa manis, rasa pahit, flavour bawang, after taste rasa pahit, serta kesukaan keseluruhan. Black garlic yang diperoleh dari penelitian ini memiliki aktivitas antioksidan tertinggi pada perlakuan lama pemeraman 16 hari dengan variasi bawang garlic yaitu memiliki aktivitas antioksidan 69,87%, kadar air sebesar 19,61%, kadar total fenol sebesar 2,67%, kadar gula total sebesar 19,58%, dan dengan uji sensoris tekstur lembut memiliki nilai 2,80, rasa manis 1,96, rasa pahit 2,39, flavour bawang 2,25, serta after taste rasa pahit 1,96, hasil yang banyak disukai oleh konsumen yaitu pada perlakuan lama pemeraman 8 hari menggunakan variasi jenis bawang lanang dengan nilai 2,13.Kata kunci: Antioksidan, black garlic, bawang. ABSTRACT Black garlic to research this alleged to have antioxidant content a high so that it can become new product of a kind of garlic that serves hinder free radicals in the body. Determine kinds of onion that produces antioxidant activity higher after going through proes warming black garlic. This study design random use of complete two factorials, by a factor first long warming 65-850c, with the temperature treatment as long as 8, 12, 16 day and the second variation kinds of onion, onions garlic, onions kating, whole onions. Chemical analysis, the antioxidant activity, water level, total phenol, sugar total and the sensory a creamy texture, sweet taste, bitter taste, berlainan onions, after taste bitter, and the favorite. The yield black garlic of the study these that have the highest antioxidant activity obtained from old treatment being handed out warm 16 day with the variation of onions garlic having the same antioxidant activity 69,87% , the moisture content of as much as 19,61% , the nature of all that the total phenol as much as 2,67 % , the action of sugar the total as much as 19,58 % , and by test sensory a creamy texture having the value of the 2,80, a sweet taste 1,96 , a bitter taste 2,39 , flavour onions 2,25 , as well as after taste was a bitter taste 1,96 , a series of poor results much liked by the consumer such it will be on a treatment long warm 8 day employing variations kinds of whole onion with a value of up 2,13.Keywords: Antioxidant, black garlic, onions