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Victor O. K. Li

Publications and source records attributed to Victor O. K. Li.

60 records · Page 4Linked to original sources
arXiv2014

Inconsistency of Measure-Theoretic Probability

We reveal a contradiction in measure-theoretic probability. The contradiction is an "equation" $1/2 = 0$ with its two sides representing probabilities. Unlike known paradoxes in mathematics, the revealed contradiction cannot be explained away and actually indicates that measure-theoretic probability is inconsistent. Appearing only in the theory, the contradiction does not exist in the physical world. So practical applications of measure-theoretic probability will not be affected by the inconsistency as long as "ideal events" in the theory (which will never occur physically) are not mistaken for real events in the physical world. Nevertheless, the inconsistency must be resolved. Constructive mathematics can avoid such inconsistency. There is no contradiction reported in constructive mathematics.

math.GM↗
arXiv2014

Opportunistic Routing for the Vehicular Energy Network

Vehicular energy network (VEN) is a vehicular network which can transport energy over a large geographical area by means of electric vehicles (EVs). In the near future, an abundance of EVs, plentiful generation of the renewables, and mature wireless energy transfer and vehicular communication technologies will expedite the realization of VEN. To transmit energy from a source to a destination, we need to establish energy paths, which are composed of segments of vehicular routes, while satisfying various design objectives. In this paper, we develop a method to construct all energy paths for a particular energy source-destination pair, followed by some analytical results of the method. We describe how to utilize the energy paths to develop optimization models for different design goals and propose two solutions. We also develop a heuristic for the power loss minimization problem. We compare the performance of the three solution methods with artificial and real-world traffic networks and provide a comprehensive comparison in terms of solution quality, computation time, solvable problem size, and applicability. This paper lays the foundations of VEN routing.

eess.SY↗
arXiv2014

Information-Theoretic Bounds for Performance of Resource-Constrained Communication Systems

Resource-constrained systems are prevalent in communications. Such a system is composed of many components but only some of them can be allocated with resources such as time slots. According to the amount of information about the system, algorithms are employed to allocate resources and the overall system performance depends on the result of resource allocation. We do not always have complete information, and thus, the system performance may not be satisfactory. In this work, we propose a general model for the resource-constrained communication systems. We draw the relationship between system information and performance and derive the performance bounds for the optimal algorithm for the system. This gives the expected performance corresponding to the available information, and we can determine if we should put more efforts to collect more accurate information before actually constructing an algorithm for the system. Several examples of applications in communications to the model are also given.

cs.IT↗
arXiv2007

Current Mathematics Appears to Be Inconsistent

We show that some mathematical results and their negations are both deducible. The derived contradictions indicate the inconsistency of current mathematics. This paper is an updated version of arXiv:math/0606635v3 with additional results and proofs.

math.GM↗
arXiv2005

Copenhagen Interpretation of Quantum Mechanics Is Incorrect

(A point-by-point response to a comment (quant-ph/0509130) on our paper (quant-ph/0509089) is added as Appendix C. We find the comment incorrect.) Einstein's criticism of the Copenhagen interpretation of quantum mechanics is an important part of his legacy. Although most physicists consider Einstein's criticism technically unfounded, we show that the Copenhagen interpretation is actually incorrect, since Born's probability explanation of the wave function is incorrect due to a false assumption on "continuous probabilities" in modern probability theory. "Continuous probability" means a "probability measure" that can take every value in a subinterval of the unit interval (0, 1). We prove that such "continuous probabilities" are invalid. Since Bell's inequality also assumes "continuous probabilities", the result of the experimental test of Bell's inequality is not evidence supporting the Copenhagen interpretation. Although successful applications of quantum mechanics and explanation of quantum phenomena do not necessarily rely on the Copenhagen interpretation, the question asked by Einstein 70 years ago, i.e., whether a complete description of reality exists, still remains open.

quant-ph↗