Hasil untuk "Mathematics"

Pak-Sing Choi, Félix Muñoz-García

Auctions have become an important mechanism to allocate scarce resources, in the physical world and in the virtual world. The analysis of auction often proceeds by assuming an ex-ante symmetry among the bidders. Yet, many markets are distinguished by fundamental asymmetries between the bidders. Some bidders may have on average higher valuations or better information, or may have a richer strategy sets. Until today very little is known how classic auction results perform in such asymmetric environments. This research project aims to develop the first such results. The research project is using advanced mathematics in optimization and differential equations, and thus will require an advanced background in mathematics, and might be ideal for majors in mathematics and joint majors in mathematics.

T. Björk

The fourth edition of this textbook on pricing and hedging of financial derivatives, now also including dynamic equilibrium theory, continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous time arbitrage pricing of financial derivatives, including stochastic optimal control theory and optimal stopping theory, the book is designed for graduate students in economics and mathematics, and combines the necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. All concepts and ideas are discussed, not only from a mathematics point of view, but the mathematical theory is also always supplemented with lots of intuitive economic arguments. In the substantially extended fourth edition Tomas Björk has added completely new chapters on incomplete markets, treating such topics as the Esscher transform, the minimal martingale measure, f-divergences, optimal investment theory for incomplete markets, and good deal bounds. There is also an entirely new part of the book presenting dynamic equilibrium theory. This includes several chapters on unit net supply endowments models, and the Cox–Ingersoll–Ross equilibrium factor model (including the CIR equilibrium interest rate model). Providing two full treatments of arbitrage theory—the classical delta hedging approach and the modern martingale approach—the book is written in such a way that these approaches can be studied independently of each other, thus providing the less mathematically oriented reader with a self-contained introduction to arbitrage theory and equilibrium theory, while at the same time allowing the more advanced student to see the full theory in action.

Manuel Santos-Trigo, Z. Gooya

The program was designed to set up to organize, structure, and discuss the academic agenda of mathematical problem solving and its developments. The program included an open invitation to the mathematics education community to contribute and reflect on research and practicing issues that involve: (a) Addressing the origin, characterization, and foundation of mathematical problem solving, (b) discussing problem solving frameworks used to support research and curricula reforms in mathematical problem solving; (c) analyzing local and international research programs in mathematical problem solving; (d) discussing curriculum proposals that support the development of mathematical problem solving; (e) analyzing different ways to assess mathematical problem solving performances; (f) discussing the role played by the use of different digital tools in students’ development of mathematical problem solving proficiency; (g) addressing programs that foster learners’ development of problem solving approaches beyond school; and (h) identifying future developments of the field.

Michael Elad

J. Baumert, Mareike Kunter, W. Blum et al.

Herbert Edelsbrunner, J. Harer

J. Bondy, U. Murty

A. Toselli, O. Widlund

C. Aliprantis, Kim C. Border

D. Lozier

J. Tits, J. Stillwell

The word "symmetry" is used in mathematics quite differently from in ordinary speech. In everyday life one applies it mainly to two-sided, right-left symmetry; but not so in mathematics. Admittedly, the word sometimes has a more general meaning in everyday speech. For example, everyone recognises that Figure 1 is highly symmetric, although it has no two-sided symmetry. However, this is really an exception. (The example of Figure 1 calls for some comment: in preparing this lecture it struck me that one can easily run into political or religious symbols when seeking examples of highly symmetric figures. This shows that symmetry has always had a powerful effect on people.)

Lindsay Smith

P. Francesco, P. Mathieu, D. Sénéchal

J. Mendel, R. John, Feilong Liu

D. Turcotte

A. Troelstra, D. Dalen, A. Heyting

Zetao Yan

Portfolio optimization is a process that involves distribution of capital with the purpose of maximizing returns and at the same time minimizing risks. The current paper discusses the use of Transformer networks in supervised learning for portfolio optimization which can set new standards for machine learning-based investment strategies. The experiments show that the portfolio management method that utilizes attention mechanisms goes beyond traditional optimization methods with a substantial difference. The performance of the recommended model in terms of average annualized return and Sharpe ratio was 24.8% and 1.69 respectively over the 14 test cases. These are considerable improvements over the benchmark strategies like equal-weighted portfolios (Sharpe ratio: 0.54), market capitalization-weighted portfolios (Sharpe ratio: 0.43), and traditional index portfolios (Sharpe ratio: 0.37). The attention mechanism is what makes the model able to dynamically adjust the portfolio weights according to the changing market forces, thus, it can blend active and passive investments efficiently. Moreover, it managed to maintain a very good risk control capacity with a Sortino ratio of 2.45 while its performance during market volatility was still quite good. So, this research serves to provide both quantitative finance and machine learning with a proof that the novel deep learning architectures can easily beat the conventional portfolio optimization methods, even in the case of small asset pools.

Shihao Zhang, Yanhui Xiao, Huawei Tian et al.

Abstract Unlike single-image steganography, the scheme of payload distribution on different images plays a pivotal role in the security performance of multi-image steganography. In this paper, a novel multi-image steganography scheme: image stitching sender (ISS) is proposed, which achieves optimal payload distribution by optimizing the stitching scheme of multi-cover-images. In the ISS scheme, we employ peak signal-to-noise ratio as the similarity evaluation metric for the stitched cover image and stego image. Besides, genetic algorithm is used to find the local optimal solution for the similarity, corresponding to a locally optimal multi-image steganographic stitching scheme. The experiment demonstrates that ISS exhibits enhanced anti-detection capabilities in comparison to other multi-image steganography schemes. Furthermore, when combined with non-additive embedding methods, the ISS can achieve a more substantial improvement in security compared to additive embedding methods.

Ibrahim Abbas, Aboelnour Abdalla, Areej Almuneef et al.

This study investigates generalized thermoelastic interaction in porous asphaltic materials subjected to thermal loading, using fractional model with time-delay effects. The framework incorporates the Riemann-Liouville fractional derivative to account for memory-dependent heat conduction, extending classical thermoelasticity into a more accurate and comprehensive domain. The Lord–Shulman model with one relaxation time is adopted to describe the coupling between mechanical and thermal responses. The governing equations are solved using Laplace transform and the eigenvalues approach, and the Stehfest algorithm is employed for numerical inversion. A detailed analysis is presented for temperature distribution, displacement, and stress fields in both solid and liquid phases of the porous medium under traction-free and thermally loaded boundary conditions. The numerical calculations show how the different sets of fractional parameters have impacted the temperature, stress, and displacement in the solid and liquid phases. Eventually, the visual representation of the data illustrates the distinctions between the fractional poro-thermoelasticity and classical coupled thermoelasticity formulations.

Oguz Emrah Turgut, Mustafa Asker, Hayrullah Bilgeran Yesiloz et al.

This theoretical research study proposes a novel hybrid algorithm that integrates an improved quasi-dynamical oppositional learning mutation scheme into the Mountain Gazelle Optimization method, augmented with chaotic sequences, for the thermal and economical design of a shell-and-tube heat exchanger operating with nanofluids. The Mountain Gazelle Optimizer is a recently developed metaheuristic algorithm that simulates the foraging behaviors of Mountain Gazelles. However, it suffers from premature convergence due to an imbalance between its exploration and exploitation mechanisms. A two-step improvement procedure is implemented to enhance the overall search efficiency of the original algorithm. The first step concerns substituting uniformly random numbers with chaotic numbers to refine the solution quality to better standards. The second step is to develop a novel manipulation equation that integrates different variants of quasi-dynamic oppositional learning search schemes, guided by a novel intelligently devised adaptive switch mechanism. The efficiency of the proposed algorithm is evaluated using the challenging benchmark functions from various CEC competitions. Finally, the thermo-economic design of a shell-and-tube heat exchanger operated with different nanoparticles is solved by the proposed improved metaheuristic algorithm to obtain the optimal design configuration. The predictive results indicate that using water + SiO₂ instead of ordinary water as the refrigerant on the tube side of the heat exchanger reduces the total cost by 16.3%, offering the most cost-effective design among the configurations compared. These findings align with the demonstration of how biologically inspired metaheuristic algorithms can be successfully applied to engineering design.