Monotone matrix functions of successive orders

This paper extends a result obtained by Wigner and von Neumann. We prove that a non-constant real-valued function, f(x), in C^3(I) where I is an interval of the real line, is a monotone matrix function of order n+1 on I if and only if a related, modified function gx0 (x) is a monotone matrix function of order n for every value of x0 in I, assuming that f' is strictly positive on I

Effect of CNT-based resin modification on the mechanical properties of polymer composites

In this study an attempt was made to explore the possibility of substituting 3D E-glass fabric with eco-friendly basalt fabric along with the modification of resin using MWCNTs, a material system about which very limited information exists. The study involved comparing the mechanical properties of two sets of composites. The first set was comprised of 3D orthogonally woven E-glass-reinforced epoxy composites, basalt-reinforced epoxy composites, and hybrid 3D E-glass orthogonally woven/basalt-reinforced epoxy composites while the second set of composites was the same as the first but prepared with resin modified with Multi Walled Carbon Nanotubes (MWCNTs). All the composites were fabricated by hand lay-up and compression molding techniques. To modify the resin for the second set of composites, MWCNTs were dispersed into the epoxy resin with acetone as a surfactant by magnetic stirring and ultra-sonification. Mechanical tests included tensile, flexural, and low velocity impact strength which were evaluated as per standards. Scanning electron microscopy (SEM) was employed to study the fractured surfaces. Results showed that resin modification did not yield any positive results on the mechanical properties of the composites. The highest tensile (364.4 MPa) and flexural strength (345.3 MPa) was obtained for 3D E-glass composites followed by basalt composites and hybrid 3D E-glass/basalt composites while the highest impact strength of 198.42 kJ/m2 was exhibited by the hybrid 3D E-glass/basalt composites. SEM micrographs showed de-bonding between the modified matrix and fiber which was seen as one of the primary causes for relatively poor performance of the composites prepared with modified resin. Fiber breakage, matrix cracking, fiber pull-out, and delamination were the other modes of failure. Results suggest that hybridization with basalt fibers is a much safer, more cost effective, and eco-friendly option over resin modification

Influence of fabric orientation and compression factor on the mechanical properties of 3D E-glass reinforced epoxy composites

3-D E-glass fabric reinforced epoxy composites at 6 mm thickness were fabricated for various orientations of the binder yarn viz. 0°, 30°, 45°, 60° and 90° respectively. Tensile, flexural, interlaminar shear stress tests were conducted to ascertain the influence of binder yarn orientation on the mechanical properties of the composites. The composites with 0° binder yarn orientation showed the best strength followed by 90° whilst the others showed highly depleted traits in comparison. Shear stress induced at the interface of each lamina was seen as the major reason for drop in the strength. A secondary study was carried out to explore the effect of compression factor during fabrication on the mechanical properties of the composites. Laminates with varying thickness namely, 4 mm, 5 mm and 7 mm but, with same number of plies of 3D E-glass fabric at 0° orientation were fabricated. The test results were compared with the results of 6 mm composites from the primary study. The results showed that, compression factor affected the mechanical properties of the composites and had a direct relation with increasing compression factor up to a certain value beyond which a drop in properties was seen. Composites pressed to a thickness of 5 mm showed the best properties. Drop in properties was attributed to close packing of reinforcement and crushing of fibres leading to inefficient stress transfer. Scanning electron microscopy was employed to understand the modes of failure. The major failure modes observed were delamination, matrix cracking and debonding. Based on the results obtained, these composites can be seen as a material system for applications like ballistic armours, structural renovations and automobile components

BLOOM: A 176B-Parameter Open-Access Multilingual Language Model

Large language models (LLMs) have been shown to be able to perform new tasks based on a few demonstrations or natural language instructions. While these capabilities have led to widespread adoption, most LLMs are developed by resource-rich organizations and are frequently kept from the public. As a step towards democratizing this powerful technology, we present BLOOM, a 176B-parameter open-access language model designed and built thanks to a collaboration of hundreds of researchers. BLOOM is a decoder-only Transformer language model that was trained on the ROOTS corpus, a dataset comprising hundreds of sources in 46 natural and 13 programming languages (59 in total). We find that BLOOM achieves competitive performance on a wide variety of benchmarks, with stronger results after undergoing multitask prompted finetuning. To facilitate future research and applications using LLMs, we publicly release our models and code under the Responsible AI License

AN EQUILIBRIUM-BASED MODEL OF STOCK-PINNING

We consider a model of the economy that splits investors into two groups. One group (the reference traders) trades an underlying asset according to the difference in realized returns between that asset and some evolving consensus estimate of those returns; the other group (hedgers) hedge options, namely straddles, on the underlying asset. We consider the cases when hedgers are long the straddle and when the hedgers are short the straddle. We numerically simulate the terminal distribution of the underlying asset price and find that hedgers that are long the straddle tend to push the underlying toward the strike, while hedgers that are short the straddle cause the underlying security to have a bimodal terminal probability distribution with a local minimum at the strike.Stock-pinning, feedback effects, hedging, equilibrium

Market Influence of Portfolio Optimizers

The paper reports on a study of the feedback effects induced by portfolio optimizers on the underlying asset prices. Through their interaction with reference traders, who trade based on some aggregate incomes process, they are assumed to move asset prices away from the standard log-normal model. With market clearing as the main constraint, the approximate dynamics of the asset price are solved analytically assuming that the wealth of the portfolio optimizers is small relative to the total market capitalization of the stock. The influence of portfolio optimizers when their wealth is not so small is also calculated numerically. There is good agreement between the numerical and analytical results when the wealth of the optimizers is small. It is found that portfolio optimizers influence the price of the risky asset so as to decrease its volatility. The optimal allocation to the risky asset also changes as a result of the portfolio optimizers' actions. In general, it is advantageous to hold more of the risky asset, relative to the log normal Merton model.Hamilton-Jacobi-Bellman equation, feedback, portfolio optimization,