Congruences and Canonical Forms for a Positive Matrix: Application to the Schweinler-Wigner Extremum Principle

It is shown that a $N\times N$ real symmetric [complex hermitian] positive definite matrix $V$ is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in $SO(m,n)$ [ $SU(m,n)$], for any choice of partition $N=m+n$. It is further shown that the method of proof in this context can easily be adapted to obtain a rather simple proof of Williamson's theorem which states that if $N$ is even then $V$ is congruent also to a diagonal matrix modulo a symplectic matrix in $Sp(N,{\cal R})$ [$Sp(N,{\cal C})$]. Applications of these results considered include a generalization of the Schweinler-Wigner method of `orthogonalization based on an extremum principle' to construct pseudo-orthogonal and symplectic bases from a given set of linearly independent vectors.Comment: 7 pages, latex, no figure

Hilbert von Neumann modules

We introduce a way of regarding Hilbert von Neumann modules as spaces of operators between Hilbert space, not unlike [Skei], but in an apparently much simpler manner and involving far less machinery. We verify that our definition is equivalent to that of [Skei], by verifying the `Riesz lemma' or what is called `self-duality' in [Skei]. An advantage with our approach is that we can totally side-step the need to go through $C^*$-modules and avoid the two stages of completion - first in norm, then in the strong operator topology - involved in the former approach. We establish the analogue of the Stinespring dilation theorem for Hilbert von Neumann bimodules, and we develop our version of `internal tensor products' which we refer to as Connes fusion for obvious reasons. In our discussion of examples, we examine the bimodules arising from automorphisms of von Neumann algebras, verify that fusion of bimodules corresponds to composition of automorphisms in this case, and that the isomorphism class of such a bimodule depends only on the inner conjugacy class of the automorphism. We also relate Jones' basic construction to the Stinespring dilation associated to the conditional expectation onto a finite-index inclusion (by invoking the uniqueness assertion regarding the latter).Comment: 20 page

Real-time Measurement of Stress and Damage Evolution During Initial Lithiation of Crystalline Silicon

Crystalline to amorphous phase transformation during initial lithiation in (100) silicon-wafers is studied in an electrochemical cell with lithium metal as the counter and reference electrode. It is demonstrated that severe stress jumps across the phase boundary lead to fracture and damage, which is an essential consideration in designing silicon based anodes for lithium ion batteries. During initial lithiation, a moving phase boundary advances into the wafer starting from the surface facing the lithium electrode, transforming crystalline silicon into amorphous LixSi. The resulting biaxial compressive stress in the amorphous layer is measured in situ and it was observed to be ca. 0.5 GPa. HRTEM images reveal that the crystalline-amorphous phase boundary is very sharp, with a thickness of ~ 1 nm. Upon delithiation, the stress rapidly reverses, becomes tensile and the amorphous layer begins to deform plastically at around 0.5 GPa. With continued delithiation, the yield stress increases in magnitude, culminating in sudden fracture of the amorphous layer into micro-fragments and the cracks extend into the underlying crystalline silicon.Comment: 12 pages, 5 figure

Web Service Deployment for Selecting a Right Steganography Scheme for Optimizing Both the Capacity and the Detectable Distortion

The principal objective of this effort is to organize a network facility to hide the secret information in an image folder without disturbing its originality. In the literature lot of algorithms are there to hide the information in an image file but most of it consumes high resource for completing the task which is not suitable for light weight mobile devices. Few basic algorithms like 1LSB, 2LSB and 3LSB methods in the literature are suitable for mobile devices since the computational complexity is very low. But, these methods either lack in maintaining the originality of the source image or in increasing the number of bits to be fixed. Furthermore, every algorithm in the literature has its own merits and demerits and we cannot predict which algorithm is best or worst since, based on the parameters such as size of the safety duplicate and encryption algorithm used to generate the cipher text the steganography schemes may produce best or worst result with respect to computational complexity, capacity, and detectable distortion. In our proposed work, we have developed a web service that takes cover image and plain text as the input from the clients and returns the steganoimage to the clients. The steganoimage will be generated by our proposed work by analyzing the above said parameters and by applying the right steganography scheme. The proposed work helps in reducing the detectable distortion, computational complexity of the client device, and in increasing the capacity. The experimental result says that, the proposed system performs better than the legacy schemes with respect to capacity, computational complexity, and detectable distortion. This proposed work is more useful to the client devices with very low computational resource since all the computational tasks are deployed in the server side

Storable Hypergolic Solid Fuel for Hybrid Rocket Engines

A solid fuel was synthesised by condensing aniline with furfuraldehyde. The product was directly cast in the rocket motor casing. After curing a hard solid mass was obtained. This was found to have good hypergolicity with RFNA (Red Fuming Nitric Acid), good storability at room temperature and the mechanical properties. The paper presented the techniques of casting, ignition delay measurements and indicates the future programme for this study