Sequences in a fuzzy metric space

AbstractIn this paper, we introduce the concept of bounded sequences in a fuzzy metric space X, d, Min, Max) and show that every convergent sequence in X is bounded. We also discuss the space of convergent sequences in a complete fuzzy metric space (X, d, Min, Max)

Computerize data information for architecture design

Computer-aided architectural design is technically and commercially feasible yet experience in the architectural profession to date is paradoxical. Many who apply computers to architecture appear satisfied but the tangible benefits are seldom obvious and even where computers are used in firms it is not done to the fullest potential. Contents of this thesis are an attempt to help architecture better utilize the advantages of computer applications.To do this it is important to examine two question: what is design and what is the computer? They are similar yet distinct. Architectural design is a special kind of problem solving process; an information processing task. Design is the organization and processing of information. Computers are electronic devices capable of storing data in an internal memory, as well as storing sets of instructions (known as programs) that operate upon data. The minds behind design accomplish similar ends with different means. The difficulty of designers solving problems is proportional to the volume of data to be handled and the quantity of interconnected relationships between functions. Various types of computers and soft-wares are available to help handle large volumes of signs and data, and help operate them according to instructions. The output of processing may be in written or graphic form and is meant to assist us in analyzing complicated problems and making decisions. It can even lead to new forms of analysis and planning. Computerization of production-information procedures such as computer selection and combination of standard details, computer produced schedules and drawings, and computer aided information retrieval, should drastically reduce the amount of effort needed in the process. New patterns of organization of the design process must then inevitably arise from such drastic changes

A note on convex functions

In this paper, we give two weak conditions for a lower semi-continuous function on the n-dimensional Euclidean space Rn to be a convex function. We also present some results for convex functions, strictly convex functions, and quasi-convex functions

Analyzing the influences of bicycle suspension systems on pedaling forces and human body vibration

Front and rear suspensions are commonly equipped on bicycles for the purpose of riding comfort especially for mountain bicycle. Suspension system includes damper for shock absorbing and spring for rebounding. Therefore suspension system would increase leg muscle forces for riding bicycle since damper dissipates some energy. ADAMS‎®‎/LifeMOD‎®‎ are proposed in this research to establish a bicycle-human integrated multibody dynamic model to investigate the impact of bicycle suspensions on cyclist’s leg muscle forces under various pedaling conditions and human body vibration for evaluation of riding comfort. Muscles studied include adductor magnus, rectus femoris, vastus lateralis and semitendinosus. Comfort analyses include the vibrating acceleration in vertical direction of lower torso and scapula. Pedaling conditions include riding on flat road, over a road bump, and climbing slope. The results indicate that suspension system increases the pedaling forces of vastus lateralis and semitendinosus. However suspension system decreases the pedaling forces of adductor magnus and rectus femoris. Suspension systems, especially the rear suspension, may effectively reduce human body vibrating acceleration. The integrated model built in this research may be used as reference for designing bicycle suspension systems. Also, the results of this study may be used as a basis of leg weight training to strengthen certain muscles for long-distance off-road cyclists

Simulation of Riding a Full Suspension Bicycle for Analyzing Comfort and Pedaling Force

AbstractRecently, there is an increasing interest on bicycle riding for recreation or fitness purpose. Bicycles are also accepted as urban transportation due to the consciousness of environmental protection. For a more comfortable riding experience, many bicycles are equipped with a suspension system including a front suspension fork and/or rear suspension. However, when a suspension system is added to a bicycle, it makes riding a little heavier since suspension dissipates some pedalling energy. This paper discusses front and rear suspensions corresponding to rider comfort and pedalling effort when riding on a rough road and smooth road. A human body computer model LifeMOD® is employed to model the cyclist. Dynamic analysis software ADAMS® is employed to analyze human body vibration and leg muscle forces of bicycle riding. Human body acceleration vs. vibration frequencies are used as the comfort criteria. The results show that a suspension system may effectively reduce high frequency vibration of the human body when riding on a rough road. Pedalling forces are mostly contributed by the biceps femoris and semitendinosus. The suspension system would increase the pedaling forces of femoris and semitendinosus. Other leg muscles have a minor effect on pedaling forces. Results obtained from this research are useful for the design of bicycle suspension systems with better comfort and less loss of pedalling efficiency

Origins of perturbations in dayside equatorial ground magnetograms

To determine the cause(s) of perturbations seen in dayside equatorial ground magnetograms, we conducted a systematic survey of simultaneous ground-based and geosynchronous satellite-based observations during the 90-day period from December 1, 2020 to February 28, 2021. We examined Huancayo ground magnetometer observations from 14:00:00 to 20:00:00 UT each day, during which Huancayo passed through local noon. From those data we chose perturbation events selected on the basis of large (>20 nT) event amplitude and classified the selected events as responding primarily to solar wind pressure, or to variations in the north/south component of the interplanetary magnetic field (IMF Bz), or perhaps in part to both. The results show that an equivalent number of events were identified for each model during this 90-day period. Variations in the lagged solar wind dynamic pressure routinely correspond to nearly simultaneous sudden impulses recorded at both geosynchronous orbit and on the ground. Variations in IMF Bz produce erosion signatures at geosynchronous orbit and can correspond to ground events if lag times for reconnection to enhance convection in the magnetosphere are taken into account

Continuity for s-convex fuzzy processes

In a previous paper we introduced the concept of s-convex fuzzy mapping and established some properties. In this work we study the continuity for s-convex fuzzy processes

Generalized preinvex functions and their applications

A class of function called sub-b-s-preinvex function is defined as a generalization of s-convex and b-preinvex functions, and some of its basic properties are presented here. The sufficient conditions of optimality for unconstrainded and inquality constrained programming are discussed under the sub-b-s-preinvexity. Moreover, some new inequalities of the Hermite—Hadamard type for differentiable sub-b-s-preinvex functions are presented. Examples of applications of these inequalities are shown