Some q-Identities derived by the ordinary derivative operator

In this paper, we investigate applications of the ordinary derivative operator, instead of the $q$-derivative operator, to the theory of $q$-series. As main results, many new summation and transformation formulas are established which are closely related to some well-known formulas such as the $q$-binomial theorem, Ramanujan's ${}_1\psi_1$ formula, the quintuple product identity, Gasper's $q$-Clausen product formula, and Rogers' ${}_6\phi_5$ formula, etc. Among these results is a finite form of the Rogers-Ramanujan identity and a short way to Eisenstein's theorem on Lambert series.Comment: 22 page

Effects of syndication network on specialisation and performance of venture capital firms

The Chinese venture capital (VC) market is a young and rapidly expanding financial subsector. Gaining a deeper understanding of the investment behaviours of VC firms is crucial for the development of a more sustainable and healthier market and economy. Contrasting evidence supports that either specialisation or diversification helps to achieve a better investment performance. However, the impact of the syndication network is overlooked. Syndication network has a great influence on the propagation of information and trust. By exploiting an authoritative VC dataset of thirty-five-year investment information in China, we construct a joint-investment network of VC firms and analyse the effects of syndication and diversification on specialisation and investment performance. There is a clear correlation between the syndication network degree and specialisation level of VC firms, which implies that the well-connected VC firms are diversified. More connections generally bring about more information or other resources, and VC firms are more likely to enter a new stage or industry with some new co-investing VC firms when compared to a randomised null model. Moreover, autocorrelation analysis of both specialisation and success rate on the syndication network indicates that clustering of similar VC firms is roughly limited to the secondary neighbourhood. When analysing local clustering patterns, we discover that, contrary to popular beliefs, there is no apparent successful club of investors. In contrast, investors with low success rates are more likely to cluster. Our discoveries enrich the understanding of VC investment behaviours and can assist policymakers in designing better strategies to promote the development of the VC industry

Computation Tree Logic Model Checking of Multi-Agent Systems Based on Fuzzy Epistemic Interpreted Systems

Model checking is an automated formal verification method to verify whether epistemic multi-agent systems adhere to property specifications. Although there is an extensive literature on qualitative properties such as safety and liveness, there is still a lack of quantitative and uncertain property verifications for these systems. In uncertain environments, agents must make judicious decisions based on subjective epistemic. To verify epistemic and measurable properties in multi-agent systems, this paper extends fuzzy computation tree logic by introducing epistemic modalities and proposing a new Fuzzy Computation Tree Logic of Knowledge (FCTLK). We represent fuzzy multi-agent systems as distributed knowledge bases with fuzzy epistemic interpreted systems. In addition, we provide a transformation algorithm from fuzzy epistemic interpreted systems to fuzzy Kripke structures, as well as transformation rules from FCTLK formulas to Fuzzy Computation Tree Logic (FCTL) formulas. Accordingly, we transform the FCTLK model checking problem into the FCTL model checking. This enables the verification of FCTLK formulas by using the fuzzy model checking algorithm of FCTL without additional computational overheads. Finally, we present correctness proofs and complexity analyses of the proposed algorithms. Additionally, we further illustrate the practical application of our approach through an example of a train control system

Comparative Analysis of Small-Scale Organic Rankine Cycle Systems for Solar Energy Utilisation

Small-scale organic Rankine cycle (ORC) systems driven by solar energy are compared in this paper, which aims to explore the potential of power generation for domestic utilisation. A solar thermal collector was used as the heat source for a hot water storage tank. Thermal performance was then evaluated in terms of both the conventional ORC and an ORC using thermal driven pump (TDP). It is established that the solar ORC using TDP has a superior performance to the conventional ORC under most working conditions. Results demonstrate that power output of the ORC using TDP ranges from 72 W to 82 W with the increase of evaporating temperature, which shows an improvement of up to 3.3% at a 100 °C evaporating temperature when compared with the power output of the conventional ORC. Energy and exergy efficiencies of the ORC using TDP increase from 11.3% to 12.6% and from 45.8% to 51.3% when the evaporating temperature increases from 75 °C to 100 °C. The efficiency of the ORC using TDP is improved by up to 3.27%. Additionally, the exergy destruction using TDP can be reduced in the evaporator and condenser. The highest exergy efficiency in the evaporator is 96.9%, an improvement of 62% in comparison with that of the conventional ORC, i.e., 59.9%. Thus, the small-scale solar ORC system using TDP is more promising for household application

The Synthesis of (E)-4-Thio-5-(2-Bromovinyl)Uridine/Deoxyuridine and Its Characterization and Cytotoxicity

(E)-4-Thio-5-(2-brominevinyl)uridine/2'-deoxyuridine(8a/8b) were efficiently and in an environmental friendly way synthesized from uridine/2'-deoxyuridine (1a/1b) that were first transformed to (E)-(2-brominevinyl) uridine / 2'-deoxyuridine(5a/5b) via iodination, selective oxidation, Heck reaction steps. The resulting products (5a/5b) were then converted to the targets (8a/8b) through esterification, thio-reaction of carbonyl, hydrolysis steps. Two new compounds (8a/8b) and three new intermediates (7a 7b 10) were obtained, and their structures have been fully characterized by 1H NMR, 13C NMR, IR, UV, HR-MS, X-Ray. The study of 8a and their derivatives regarding cytotoxicity was carried out by using MTT experiment method, and the initial findings suggest (E)-4-Thio-5-(2-brominevinyl) uridine/ 2'-deoxyuridine (8a / 8b) would be potential antitumor drugs

Identity-Set-based Broadcast Encryption supporting “Cut-or-Select” with Short Ciphertext

In this paper we present an identity-set-based broadcast encryption scheme with three working modes: positive membership (Select-mode), all member (All-mode), and negative membership (Cut-mode) over the user identity set, simultaneously.The core of our scheme is the implementation of cryptographic representation of subset by using two aggregation functions: Zeros-based aggregation and Poles-based aggregation. These two aggregation functions are capable of compressing any subset into one element in a bilinear map group for determining the membership between an element and a subset. Our scheme achieves the optimal bound of O(1)-size for either ciphertext (consisting of just two elements) or decryption key (one element) for an identity set of large size. We prove that our scheme is secure under the General Diffie-Hellman Exponent (GDHE) assumption

Intelligent Reflecting Surface Aided Multi-Tier Hybrid Computing

The Digital twin edge network (DITEN) aims to integrate mobile edge computing (MEC) and digital twin (DT) to provide real-time system configuration and flexible resource allocation for the sixth-generation network. This paper investigates an intelligent reflecting surface (IRS)-aided multi-tier hybrid computing system that can achieve mutual benefits for DT and MEC in the DITEN. For the first time, this paper presents the opportunity to realize the network-wide convergence of DT and MEC. In the considered system, specifically, over-the-air computation (AirComp) is employed to monitor the status of the DT system, while MEC is performed with the assistance of DT to provide low-latency computing services. Besides, the IRS is utilized to enhance signal transmission and mitigate interference among heterogeneous nodes. We propose a framework for designing the hybrid computing system, aiming to maximize the sum computation rate under communication and computation resources constraints. To tackle the non-convex optimization problem, alternative optimization and successive convex approximation techniques are leveraged to decouple variables and then transform the problem into a more tractable form. Simulation results verify the effectiveness of the proposed algorithm and demonstrate the IRS can significantly improve the system performance with appropriate phase shift configurations. Moreover, the results indicate that the DT assisted MEC system can precisely achieve the balance between local computing and task offloading since real-time system status can be obtained with the help of DT. This paper proposes the network-wide integration of DT and MEC, then demonstrates the necessity of DT for achieving an optimal performance in DITEN systems through analysis and numerical results