The recession cone and recession function are very important research objects in Convex Analysis. They have extensive applications in the optimization theory. Firstly, we study the properties of the recession cone and recession function. The positive homogeneity and subadditivity of recession function are mainly discussed. And the different methods are considered to prove these properties. Secondly, we discuss the unboundedness of the convex sets and convex functions by using recession cone and recession function.

First principles simulation studies using the density functional theory have been performed on (9, 0) Zigzag Singlewalled Carbon Nanotube (SWCNT) to investigate its electronic, optical and thermodynamic properties using CASTEP (Cambridge Sequential Total Energy Package) and DFTB (Density Functional based Tight Binding) modules of the Material Studio Software version 7.0. Various functionals and sub-functionals available in the CASTEP Module (using Pulay Density Mixing treatment of electrons) and various eigen-solvers and smearing schemes available in the DFTB module (using smart algorithm) have been tried out to chalk out the electronic structure. The analytically deduced values of the band gap obtained were compared with the experimentally determined value reported in the literature. By comparison, combination of Anderson smearing scheme and standard diaogonalizer produced best results in DFTB module while in the CASTEP module, GGA (General Gradient approximation) functional with RPBE (Revised-perdew-Burke-Ernzerh) as Sub-functional was found to be the most consistent. These optimized parameters were then used to determine various electronic, optical and thermodynamic properties of (9, 0) Singlewalled Nanotube. (9, 0) Singlewalled Nanotube, which is extensively being used for sensing NH₃, CH₄ & NO₂, has been picked up in particular as it is reported to exhibit a finite energy band gap in contrast to its expected metallic nature. The study is of utmost significance as it not only probes and validates the simulation route for predicting suitable properties of nanomaterials but also throws light on the comparative efficacy of the different approximation and rationalization quantum mechanical techniques used in simulation studies.

Using the rank scale rule, taking 47 major port cities in China from 2001 to 2015 as research samples, this paper discusses the rank scale characteristics and hierarchical structure of coastal port city system from a multi-functional perspective, and divides the coupling type of multi-functional development based on shipping logistics. The research shows that: 1) from 2001 to 2015, the scale-free area of manufacturing function order scale distribution in the coastal port city system appeared bifractal structure, the hierarchical segmentation characteristics appeared, and the other functions were single fractal; From the perspective of long-term evolution, only the order and scale distribution of shipping logistics function has developed from centralization to equilibrium, while the business function, manufacturing function (scale-free region I), modern service function and population distribution function are in a centralized situation. 2) The hierarchical structure of coastal port city system has gradually changed from pyramid structure to spindle structure, and generally formed five levels: national hub, regional hub, regional sub center, regional node and local node. 3) From the perspective of multi-functional coupling types, the traditional functions of port cities are generally ahead, while the high-end service functions lag behind, and the improvement speed of urban functions is slow and tends to be flat, indicating that the multi-functional development of China’s coastal port cities is still at a low level, and the industrial system structure needs to be further optimized. 4) From the perspective of port cities at different levels, the functions of regional hub cities and regional sub central cities are in the stage of rapid growth; regional and local node cities are still in the growth stage of traditional functions such as industry and commerce.

The world has complex mega-cities and interdependent infrastructures. This complication in infrastructure relations makes it sensitive to disasters and failures. Cascading failure causes blackouts for the whole system of infrastructures during disasters and the lack of performance of the emergency management stakeholders is clear during a disaster due to the complexity of the system. This research aimed to develop a new concurrent engineering model following the total recovery effort. The objectives of this research were to identify the clustered intervention utilized in the field of resilience and developing a cross-functional intervention network to enhance the resilience of societies during a disaster. Content analysis was employed to classify and categorize the intervention in the main divisions and sub-divisions and the grouping of stakeholders. The transposing system was employed to develop an integrated model. The result of this research showed that the operations division achieved the highest weight of information interchange during the response to improve the resilience of the system. The committee of logistics and the committee of rescue and relief needed the widest bandwidth of information flow in the concurrent engineering (CE) model. The contributed CE model helped the stakeholders provide a resilient response system. The final model and the relative share value of exchanging information for each workgroup can speed up recovery actions. This research found that concurrent engineering (CE) is a viable concept to be implemented as a strategy for emergency management. The result of this research can help policymakers achieve a collaborative teamwork environment and to improve resilience factors during emergency circumstances for critical infrastructures.

The size effect on the free vibration and bending of a curved FG micro/nanobeam is studied in this paper. Using the Hamilton principle the differential equations and boundary conditions is derived for a nonlocal Euler-Bernoulli curved micro/nanobeam.  The material properties vary through radius direction. Using the Navier approach an analytical solution for simply supported boundary conditions is obtained where the power index law of FGM, the curved micro/nanobeam opening angle, the effect of aspect ratio and nonlocal parameter on natural frequencies and the radial and tangential displacements were analyzed. It is concluded that increasing the curved micro/nanobeam opening angle results in decreasing and increasing the frequencies and displacements, respectively. To validate the natural frequencies of curved nanobeam, when the radius of it approaches to infinity, is compared with a straight FG nanobeam and showed a good agreement.

Catastrophes, like earthquakes, bring sudden and severe damage, causing fatalities, injuries, and property loss. This often triggers a rapid increase in insurance claims. These claims can encompass various types, such as life insurance claims for deaths, health insurance claims for injuries, and general insurance claims for property damage. For insurers offering multiple types of coverage, this surge in claims can pose a risk of financial losses or bankruptcy. One option for insurers is to transfer some of these risks to reinsurance companies. Reinsurance companies will assess the potential losses due to a catastrophe event, then issue catastrophe reinsurance contracts to insurance companies. This study aims to construct a valuation model for catastrophe reinsurance contracts that can cover claim losses arising from two types of insurance products. Valuation in this study is done using the Fundamental Theorem of Asset Pricing, which is the expected present value of the number of claims that occur during the reinsurance coverage period. The number of catastrophe events during the reinsurance coverage period is assumed to follow a Poisson process. Each impact of a catastrophe event, such as the number of fatalities and injuries that cause claims, is represented as random variables, and modeled using Peaks Over Threshold (POT). This study uses Clayton, Gumbel, and Frank copulas to describe various dependence characteristics between random variables. The parameters of the POT model and copula are estimated using Inference Functions for Margins method. After estimating the model parameters, Monte Carlo simulations are performed to obtain numerical solutions for the expected value of catastrophe reinsurance based on the Fundamental Theorem of Asset Pricing. The expected reinsurance value based on Monte Carlo simulations using Indonesian earthquake data from 1979–2021 is Rp 10,296,819,838.