Pi International Journal of Mathematical Sciences
PI International Journal of Mathematical Sciences PI International Journal of Mathematical Sciences (PIJMS) is an International Open Access, Peer-reviewed and Refereed Journal publishing high-quality original research papers, review articles and scholarly communications in pure and applied mathematics. The journal follows COPE Guidelines and provides immediate open access under Creative Commons Licensing. ISSN: 3107-9830 Frequency: Bimonthly Subject: Mathematics Submit Paper
In the present paper, we introduce the notion of S-Menger like space (S-MLS), which is the hybrid structure of metric like space and S-Menger space. We also given examples of (S-MLS). In the last section we prove Banach contraction principle and another unique fixed-point theorem for Menger k contractive map in the setting of S-Menger like Space.
S-Menger like space, Fixed point, Banach contraction principle.
Copyright (c) 2026 Pi International Journal of Mathematical Sciences
Analytical Study of Distance-Based Topological Indices for the Cluster Product of Km and Pn
A topological index is an analytically derived numerical quantity that characterizes the structural properties of a graph. These indices play a crucial role in chemical graph theory and quantitative structure–property/activity relationship (QSPR/QSAR) studies. In this paper, we investigate several distance-based topological indices and clusters, including the Wiener index (W), Hyper-Wiener index (WW), Harary index (H), Reciprocal Complementary Wiener index (RCW), Sum Connectivity Index (SCI), Batschelet Index (B), Reverse Wiener index (∧), Reciprocal Reverse Wiener index (R∧(G)).
Wiener index, Hyper-Wiener Index, Harary Index, Reciprocal Complementary Wiener Index, Sum Connectivity Index, Batschelet Index, Reverse Wiener Index, Reciprocal Reverse Wiener Index and Cluster Product.
Application of Input–Output Analysis in the Indian Food Processing Industry: A Case Study Approach
This work explores analytical solutions of fractional-order dispersive partial differential equations using a newly proposed decomposition approach. Fractional derivatives are formulated in the Caputo sense. The obtained solutions, for both fractional and classical integer-order cases, are expressed as convergent series, highlighting the effectiveness and fast convergence of the technique. To demonstrate the reliability and applicability of the method, several representative examples are discussed in detail. Furthermore, the study examines how the solutions of fractional-order models gradually approach the corresponding integer-order solutions as the fractional parameter varies. Keywords: Nonlocal partial differential equations (FPDEs), Dispersive equations, Caputo Nonlocal derivative, Convergence analysis, Laplace transform.
A Climatic Trend Assessment of Temperature and Precipitation in Rajasthan
Rising temperatures along with decreasing and irregular rainfall represent a major global concern. This study examines trends in temperature and rainfall across five divisional headquarters of Rajasthan—Bikaner, Jaipur, Jodhpur, Kota, and Udaipur. Historical records of minimum and maximum temperatures, as well as rainfall data spanning 50 years (1970–2020), were obtained from the Climate Research and Services of the India Meteorological Department in Pune. Trend detection and the magnitude of changes were analyzed using the Mann–Kendall (MK) test and Sen’s slope method. The findings reveal a significant upward trend in both minimum and maximum temperatures at all five locations. In contrast, rainfall exhibited a slight but statistically insignificant increase in Kota and Udaipur, while Bikaner, Jaipur, and Jodhpur showed a declining trend.
Climate Change; Temperature Trend; Rainfall Variability; Mann–Kendall Test; Sen’s Slope
A Sustainable AI-Based Inventory Optimization Framework with Carbon Cost Minimization Using Hybrid LSTM–GA–DQN
Managing inventory has become more challenging because of the fluctuation in customer demand, product deterioration, market volatility, and environmental sustainability laws. Traditional inventory optimization techniques struggle to incorporate and optimize for non-linear demand forecasts and minimize carbon emissions. Recognising these limitations, the present research proposes a sustainable framework for inventory optimization by applying different techniques such as Long Short-Term Memory (LSTM), Genetic Algorithm (GA), and Deep Q-Network (DQN). The historical relationship between demand is captured in an LSTM model to predict future demand, while the Genetic Algorithm is used for replenishment decisions and their associated safety stock levels to optimize the model. Furthermore, the DQN agent can acquire the optimal inventory policy as it moves in an unknown environment. A cost component for the carbon emissions is added to the objective function, so that sustainable green supply-chain operations are possible. The hybrid model will have the cost of holding and ordering cost will come down, there will be no shortage cost, diminishing cost, carbon emission cost, and service level & operational efficiency will be increased as a result of the hybrid model. Besides this, the model proposed here is better than the traditional inventory models from various numerical and sensitivity analysis that proves the sustainability, adaptability, and cost reduction capabilities of the model.
Sustainable Inventory, LSTM, Genetic Algorithm, Deep Q-Network, Carbon Cost Minimization, Green Supply Chain, Demand Forecasting
Transient Elastico-Viscous Boundary Layer Thermal Transport with Stagnation-Point Slip Flow Over a Stretching Surface
The unsteady boundary-layer dynamics governing momentum and thermal transport induced by a stretching surface within an elastico-viscous medium are systematically examined. The surface interaction is modelled through a non-standard partial slip formulation, facilitating a refined characterization of near-wall kinematics. The constitutive behaviour of the elastico-viscous fluid is represented via Walters’ liquid Model B′, thereby accounting for memory-dependent rheological effects. Through the imposition of judiciously selected similarity transformations, the fundamental conservation equations are transmuted into a dimensionally contracted, self-similar construct, thereby rendering the system tractable for subsequent numerical interrogation. Computational resolution of the resulting boundary-value problem is executed through MATLAB’s inbuilt collocation algorithm bvp4c, yielding velocity and thermal fields as well as ancillary transport parameters. Parametric interrogation highlights the pronounced influence of unsteadiness, surface slip, and elastico-viscosity on the emergent flow architecture. Results elucidate that the elastico-viscous modulus, velocity ratio, and both kinematic and thermal slip coefficients exert dominant control over momentum transport and heat transfer characteristics under slip and no-slip configurations. The investigation further establishes that the velocity and thermal distributions exhibit acute sensitivity to variations in the embedded flow-control parameters.
Elastico-viscous fluid; Walters’ liquid Model B′; Unsteady boundary-layer flow; Partial slip; Heat transfer.
Optimization of Inventory Costs under Exponential Deterioration, Shortage, Inflation, and Power Dependent Demand using AI- Based Techniques
This research introduces dynamic inventory model that combines exponential linear power dependent demand, in which the demand rate depends on the selling price. The model describes the reality of market behaviour in that items that decay with time are taken into account and demand changes with the decisions made on prices. In order to reflect the current economic environment, inflation is also factored in by use of present value discounting methods to allow a better evaluation of the inventory related expenses throughout the planning time frame. Particle Swarm Optimization (PSO) algorithms based on Artificial Intelligence (AI) are further used to optimize the model to find the cost minimizing inventory policy. Shortages are also allowed and are assumed to be fully backlogged, and therefore the model is applicable when delayed fulfilment is tolerated in industries. The entire numerical example is presented to show the structure of calculations and prove the efficiency of the methodology. Besides that, an analysis of the effect of the most important parameters on the total cost of the system is carried out through a sensitivity analysis; these parameters include the rate of deterioration and inflation, demand exponent, holding cost and shortage cost. The findings indicate that the joint impact of deterioration, inflation and price-sensitive demand play a significant role in optimal ordering decisions. The optimization with the use of AI provides more powerful and efficient solutions compared to the traditional mathematical methods. In general, this research may be useful to managers and practitioners who need to address perishable or deteriorating products in inflationary conditions so that they could implement cost-efficient and evidence-based decision-making procedures.
Deterioration, Inflation, Power-dependent demand, EOQ, PSO Algorithm, Shortage
On the Accuracy and Efficiency of Galerkin and Direct Methods for Second-Order Boundary Value Problems with Neumann Boundary Conditions
This study presents a numerical analysis of a second-order mixed boundary value problem with Neumann boundary condition. The problem is first formulated and solved using the Galerkin method, where the Neumann condition is naturally incorporated through weak formu-lation. To independently verify the Galerkin solution, a direct numerical approach based on a shooting technique combined with a DMVS adaptive integrator is employed, and the unknown initial derivative is determined using a secant iteration. A detailed comparison between the analytical solution, the Galerkin approximation, and the direct numerical results is carried out in terms of solution profiles, initial slope, and error norms. The numerical results demonstrate excellent agreement between both approaches, confirming the accuracy, stability, and reliability of the Galerkin formulation. The study highlights that while the direct method offers computa-tional efficiency, the Galerkin method provides a systematic and robust framework suitable for mixed boundary value problems.
Galerkin Method; Direct Numerical Method; Neumann Boundary Condition; Mixed Boundary Value Problem; Shooting Technique
A Study on Application of Input–Output Analysis in the Indian Food Processing Industry
This paper determines the links from Agriculture, forestry and fishing industry to Food and Beverages industry by the help of structural relationships associated in input-output tables. The paper develops a methodology to modify the magnitude of economic fluctuations and trace their downstream effects throughout the entire value chain. This section categories the fundamental principles of input-output analysis and gives its practical application through a simplified inter-industry transaction model, using data sourced from the Library with ADB Data, India: Input-Output economic indicators (Tables)-2020. The analysis infers that input-output frameworks streamline cost management; by requiring a precise definition of each sector's value-added function, they allow for more rigorous oversight of production inputs.
Input–Output Analysis, Food Processing Industry, Agriculture, Forestry and Fishing Sector, Leontief Model, Technology Matrix, Hawkins–Simon Conditions.
The Menger g-Contraction Maps and Menger Asymptotically g-Contraction Maps in S- Menger Space with Applications
We define Menger g-contraction and Menger asymptotically g-contraction maps with examples in this study. We have examined two coincidence point results in S-Menger space as an application of Menger g-contraction and Menger asymptotically g-contraction maps.
S-Menger space, coincidence point, Menger g-contraction and Menger asymptotically g-contraction maps
Delay Differential Equations Modelling and Stability of Tumor Growth with Immune Responses
The development of tumors is a very complicated biological process, which is controlled by various interacting factors, such as the proliferation of cells, immune system, nutrients, and treatment. Mathematical and computational modelling is an efficient method to the comprehension of the mechanisms governing tumor dynamics. In the present paper, we construct a delayed differential equation model that is used to explain the interaction between tumor cells and the responses of immune system. Linearization techniques and analysis of characteristic equations are used to analyse the model in terms of the existence of equilibrium points, stability properties of those points and the bifurcation behaviour that may occur. The results demonstrate that time delay can disrupt the otherwise steady equilibria to produce oscillating tumor dynamics, which shows the dramatic effect of the delayed immune response or treatment response on tumor dynamics.
OPTIMIZED ELLIPTIC CURVE CRYPTOGRAPHIC COMPUTATIONS USING ANCIENT INDIAN VEDIC MATHEMATICS TECHNIQUES
This study investigates the integration of Ancient Indian Vedic Mathematics (AIVM) into contemporary cryptographic frameworks, with a particular emphasis on Elliptic Curve Cryptography (ECC). Cryptographic computations in ECC require substantial computational resources and execution time, especially during core operations such as point addition, point doubling, and modular multiplication. The AIVM system, based on sixteen Sutras and fourteen Sub-sutras, offers efficient and high-speed arithmetic techniques. This paper examines the applicability and performance benefits of the Urdhva-Tiryagbhyam sutra for multiplication, the Dvandva-Yoga sutra for squaring operations, and the Nikhilam Navatashcaramam Dashatah sutra for handling large-number computations. By implementing these ancient techniques, the computational latency and hardware complexity of systems like RSA and ECC can be significantly reduced. The survey demonstrates that Vedic algorithms not only accelerate encryption and decryption processes but also optimize hardware resource utilization, making them highly suitable for high-speed security applications. Keywords: ECC, Vedic Mathematics, Dhvajanka, Cryptography, Dvandva-Yoga, Urdhva-Tiryagbhyam, Nikhilam Navatashcaramam Dashatah.
Copyright (c) 2025 Pi International Journal of Mathematical Sciences
SYSTEM COST AND RELIABILITY OPTIMIZATION THROUGH FUZZY-BASED TASK SCHEDULING IN DISTRIBUTED COMPUTING SYSTEMS
Efficient task scheduling in distributed and cloud-fog computing environments plays a pivotal role in optimizing system performance, reliability, and operational costs. This study presents a comprehensive task scheduling model that integrates cost-aware and reliability-driven strategies to enhance resource utilization while minimizing system downtime and overall execution expense. By incorporating dynamic workload distribution, fuzzy-logic-based decision-making, and hybrid metaheuristic approaches, the proposed model addresses uncertainties and heterogeneity in modern computing systems. Extensive simulations and performance analyses demonstrate that the model achieves significant improvements in system reliability and cost reduction compared to conventional scheduling techniques. The findings offer a practical framework for designing adaptive and efficient scheduling mechanisms in cloud, fog, and IoT-enabled environments. Keywords: Task Scheduling, System Reliability, Cost Optimization, Cloud Computing, Fog Computing, IoT, Fuzzy Logic, Hybrid Metaheuristics, Resource Allocation.
Integrating Sustainability into Perishable Stock Systems: A Model for Pricing and Emission Constraints
This study explores a math system for improving the stock of things that break down over time, all while dealing with current environment rules and what people think. The main aim is to balance making money with being eco-friendly, paying close attention to how prices change with stock levels and limits on carbon emissions. Unlike older plans that guess demand is steady or don't think about the environment cost of keeping and throwing away items that go bad, this looks at the whole picture. We use math equations to show how stock goes down because of sales and decay over time. The way we things look at the total cost, like carbon taxes on keeping goods and getting rid of waste. Computer tests show that a way of thinking where having stock on display boosts sales needs to be carefully balanced against faster decay and carbon fines for having too much stock. The results show that using prices that can change allows for more freedom in how much profit can be made, mainly when dealing with changes in demand. The work ends by saying that an eco-friendly plan doesn't just meet rules but makes the whole supply chain stronger by cutting down on physical losses. This gives useful ideas for managers in medicine and food who have to keep service levels high while meeting green business goals.
A Comprehensive Scheme for Approximating Fractional 3D Partial Differential Equations in Fluid Systems
Fractional calculus has attracted significant attention as a powerful tool for modeling physical and engineering systems with memory and hereditary effects. Fractional-order derivatives offer more realistic descriptions of phenomena such as anomalous diffusion, viscoelastic behavior, and wave propagation. Recent advances in analytical and numerical techniques have enabled effective treatment of fractional partial differential equations (FPDEs). In this chapter, three semi-analytical methods—Adomian Decomposition Method (ADM), Variational Iteration Method (VIM), and New Iterative Method (NIM)—are applied to obtain approximate analytical solutions of three-dimensional time-fractional diffusion, telegraph, and wave equations. These methods avoid discretization and linearization, produce rapidly convergent series solutions, and are validated through illustrative examples, demonstrating their accuracy and applicability to multidimensional time-fractional models. Keywords: Fractional calculus, Time-fractional partial differential equations, Adomian Decomposition Method (ADM), Variational Iteration Method (VIM), New Iterative Method (NIM), Diffusion equation, Telegraph equation, Wave equation, Semi-analytical methods.
PERFORMANCE ANALYSIS OF EDWARDS ELLIPTIC CURVES USING VEDIC MATHEMATICS FOR SECURE AUTHENTICATION PROTOCOLS IN ECC
In order to create effective implementations of point addition and point doubling algorithms for Edwards elliptic curves, this paper investigates the use of Vedic mathematical approaches. The goal of the suggested approach is to improve Edwards elliptic curve cryptography (ECC) procedures processing efficiency. In particular, the Urdhva-Tiryagbhyam sutra is used to optimize multiplication procedures, and the Dvandva-yoga method is used to speed up squaring operations. These methods are used to provide two optimized cryptographic formulations for Edwards elliptic curves: point addition and point doubling. In terms of execution speed, processing time, and lower multiplier power consumption, experimental evaluations show that the Vedic mathematics-based methodology performs noticeably better than traditional arithmetic methods. Point addition and scalar operations are implemented in MATLAB utilizing 16-bit and 32-bit operands. Additionally, a number of Vedic mathematical methods are examined to determine how they affect elliptic curve calculations; the findings are displayed using detailed tables and graphical representations. The results demonstrate how Vedic mathematics can significantly increase the effectiveness and performance of elliptic curve cryptography systems.
Finite field, UTT, DYT, EEC, Points addition, Point doubling.
Mathematical Optimization of an Inventory Model for Deteriorating Items with Time and Reliability-Dependent Demand
This study presents a mathematical model to better manage inventory for goods that decay over time. Standard inventory models assume demand stays the same, but this model considers that demand changes depending on time and how reliable people think the product is. Decay is figured as a set amount of the inventory, which is normal for things like medicines and electronics. The main aim is to find the best reordering time that lowers the total cost of inventory, including expenses for ordering, keeping stock, decay, and making the product seem more reliable. Using math, we find a direct answer for the total cost and show that it is cost-effective. Computer tests show that if product reliability is not considered, demand is underestimated, and ordering is not as good as it could be. The results suggest that putting money into system reliability raises initial costs but makes market demand more steady and cuts long-term decay losses. This study gives supply chain managers a helpful way to make choices in unstable markets where product quality and timing are very important.
Graph Theory and its Cryptography Applications: A Novel Approach
In our modern society werely extensively on digital technology, which plays a critical role in various sectors, including banking, e-commerce transactions and cybersecurity such as managing computer passwords. This extensive integration emphasizes the critical role of reliable and secure digital infrastructure in our day-to-day activities. Therefore, it is more important to secure information during storage and transformation. Cryptography is the process of safeguarding information by converting it in a protected form, making it accessible only to authorized users. The process employs encryption algorithms to turn simple data, or "plaintext," into a coded version, referred to as "ciphertext," making it unreadable without proper authorization. Cryptography benefits from graph theory, as it enables the seamless conversion of graphs into matrices for cryptographic operations. In numerous disciplines, Graph Theory is indispensable, especially in encryption, due to its numerous properties and its ease of implementation as a matrix in computational systems. This paper introduces a novel approach that combines graph theory with symmetric cryptography, presenting an innovative method to enhance data security and protect against unauthorized access. Keywords: Cryptography, Decryption
Graph-Based Unified Cryptographic system for Secure Communication and Financial Transactions
In today's increasingly interconnected world, ensuring the protection of digital information transmitted over unprotected communication networks —whether wired or wireless—is paramount. Encryption algorithms are central to protecting sensitive data, and hybrid encryption methods, which combine different encryption techniques, provide a stronger level of security compared to conventional single-key encryption methods.Top of FormBottom of Form Although many Unified encryption models exist, many fall short in addressing diverse security challenges. This paper proposes a novel Unified encryption scheme that combines the widely-used public key cryptosystem (RSA) algorithm, a newly introduced Secret key cryptography (SKC) algorithm, and a Graph-Based Encryption Approach. This combination aims to provide more robust data privacy, integrity, and security. We believe this enhanced model offers an effective solution for secure communication in the face of evolving cyber threats. Keywords: Cryptography, Unified Encryption, RSA, Secret Key (SKC), Graph-Based Encryption, Data Security, Information Privacy
Exploring Topological Indices of Special Graphs through Computational Techniques
By make use of the vertex degree of the graphs, the polynomials of the special graphs like Bull graphs, graphs, Butterfly graphs, and Cricket graphs were acquired and scrutinized in this paper. Also, with the help of polynomials of the abovesaid special graphs, the several vertex degree-dependent topological indices of the special graphs were also determined. Additionally, we computed the comparison table and provided a graphical representation of the determined topological indices.
M-Polynomial, Bull graphs, H-graphs, Butterfly graphs, Cricket graphs, Topological Indices.
Mathematical Propagation for the Treatment and Vaccination of a Generalized Well-Posed SEIR Infectious Model
In this paper, we proposed a generalized theoretical executable investigation for an improved SEIR mathematical model for infectious diseases. The model was constructed to determine a solution for a system of ordinary differential equations described in a deterministic immune population and studied under designated bilinear control functions. Analytic predictions for the system's well-posedness were quantitatively conducted using the theory of ordinary differential equations in conjunction with the Lipschitz condition. An expression is obtained for the state-space, and numerical computations are determined. Results show that with induced bilinear control functions, rapid rejuvenation of the recovered and the susceptible was tremendously achieved. Moreso, the model exhibited compatibility for varying infectious diseases, provided there exists coherence to designated control functions. Therefore, the application of an improved generalized SEIR model under bilinear control functions is priori innovative for the amelioration and treatment of infectious diseases when compared with the results of existing SIR models.
Generalized-SEIR-model, system-well-posedness, bilinear-control-functions, Lipschitz-condition, existence-uniqueness, state-space.
Advances in Sobolev Spaces and Their Applications to Modern Analysis and PDEs
This paper surveys recent advances in Sobolev spaces (also known as fractional-order Sobolev spaces, Besov spaces, Bessel or Riesz potential spaces, and Triebel–Lizorkin spaces) and their applications to modern analysis and partial differential equations (PDEs). The studied fractional Sobolev spaces unifying these classical spaces have proved to be useful tools in both linear and nonlinear PDE theory. Various classical tools of nonlinear analysis, including fixed point theorems, Leray–Schauder degree theory, variational methods, and blow-up arguments, have been extended to these spaces, significantly expanding their nonlinear analysis capacity. The report summarizes recent progress on fractional Sobolev spaces and related fields of nonlinear analysis, applications, nonlinear PDEs, and the Navier–Stokes equations, clarifying the advantages of employing fractional Sobolev spaces in these contexts. Keywords: Sobolev spaces, partial differential equations, linear and nonlinear
Recent Advances and Applications in Modern Number Theory: A Comprehensive Review
Number theory investigates the natural numbers and their properties. The classical disciplines of number theory treat natural numbers either as objects of investigation or as tools to solve diophantine equations. These and other ancillary theories are the staples of number theory and include prime numbers, divisibility, modular arithmetic, quadratic reciprocity, and the construction of number systems. The study of divisibility in the integers led to the introduction of the Euclidean algorithm of finding the greatest common divisor, which in turn produced the concept of a prime number. The work of Euclid develops in an elementary setting the idea of studying natural numbers and certain properties like divisibility. The modern study of number theory introduces a spiral of ideas that diverge from that of Euclid. Euclid’s original investigation looked exclusively at the integers while the more modern approach examines the integers as part of a wider algebraic setting consisting of rational, real, complex, -adic, and other algebraic integers. Moreover, instead of relying on elementary arithmetic, analysis techniques are used to illuminate the subject. The combination of analytic as well as algebraic methods culminates in the foundation of modern number theory.
A Comprehensive Review of the Coreflective Hull of T0​-Fuzzy Spaces
The construction of the coreflective hull of ????0-fuzzy topological spaces has attracted increased interest from various authors, either as a tool or as a class of spaces to study and characterise its role in the structure of the category T0-????????????????, whose objects are fuzzy ????0-topological spaces and morphisms are fuzzy continuous maps (Sibahle Nxumalo, 2019). Moreover, the class of coreflective spaces in the classical category ????????????, whose objects are topological spaces and morphisms are continuous maps, has attracted considerable attention (Sibahle Nxumalo, 2019). It is well known that the coreflective hull of the class of ????0-topological spaces coincides with the class of ????2-spaces (Hausdorff spaces). Consequently, the construction of a fuzzy ????2-space on a given fuzzy ????0-space could play a crucial role in the study of the more general coreflective hull of fuzzy ????0-topological spaces. With the aim of obtaining such a construction, we further advance the study of fuzzy ????0-spaces to the more general fuzzy ????0-spaces. Keywords: Coreflective Hull, Fuzzy ????0-Topological Spaces, Fuzzy Continuous Maps, Hausdorff Spaces (????2-Spaces), Category Theory in Topology.
Mathematical Modeling of Air Pollution Dispersion: A Comprehensive Review
Air pollution is a pressing global concern affecting human health, ecosystems, and climate dynamics. Mathematical modeling serves as a critical tool for predicting pollutant behavior and designing mitigation strategies. This paper reviews major air pollution modeling techniques, including Gaussian and advection-diffusion models, Lagrangian particle tracking, Eulerian grid systems, and hybrid approaches, alongside emerging machine learning-based prediction models. Mathematical formulations such as the advection-diffusion equation, stochastic processes, and probabilistic frameworks are discussed in detail. Applications in complex terrains, street canyon environments, and health risk modeling are explored. The review concludes with future directions focusing on real-time hybrid modeling and integration with machine learning for sustainable environmental management. Keywords: Air pollution modeling, advection-diffusion equation, Lagrangian particle model, Gaussian plume model, stochastic modeling, machine learning, environmental health risk.
Mathematical Model on Economic Loss and Load Traffic Injuries
To estimate the economic loss due to road transport and the relationship between the economic loss and human health System. It has been observed that sand accidental persons on road depend upon P, and B. Whenever pavement A load increases the road accident Over load vehicles and Bad Weather also increases road accident. Agent It is clear that accidental medical Cost increases with the influx.
load vehicles Bad Weather medical cost Insurance of reside