Abstract:
This paper deals with the estimation of the specific connectivity of a stationary random set in IRd. It turns out that the "natural" estimator is only asymptotically unbiased. The example of a boolean model of hypercubes illustrates the amplitude of the bias produced when the measurement field is relatively small with respect to the range of the random set. For that reason unbiased estimators are desired. Such an estimator can be found in the literature in the case where the measurement field is a right parallelotope. In this paper, this estimator is extended to apply to measurement fields of various shapes, and to possess a smaller variance. Finally an example from quantitative metallography (specific connectivity of a population of sintered bronze particles) is given.

Abstract:
This paper explores the effects of trade policy under induced innovation in general equilibrium. The analysis considers the effects of discrete changes in tariffs and import quotas, allowing for heterogeneous technologies among firms. The interactions between induced innovation and the effects of trade policy give a set of “LeChatelier effects” comparing short run versus long run market equilibrium. We investigate how induced innovation can reduce the adverse effects of tariffs on trade, and influence the effects of quotas on corresponding quota rents. The analysis presents new LeChatelier results that apply globally, i.e. under any discrete change in trade policy.

Three months before his untimely death in Paris in July 1912, Henri Poincaré formulated the conjecture that Planck’s action element could (should) be regarded as constituting a “véritable atome”, i.e. an “atom of motion”, whose integrity arises from the fact that the “points” it contains are equivalent to one another from the standpoint of probability. In this paper we investigate the possibility that this conjecture provides a clue to the origin and nature of dark matter.

The elementary particles listed in the Standard Model of particle
physics have all in common a quantum mechanical attribute which has the
dimension of the xon, suggestingthat the xon might be a structural ingredient
of matter. The xon should therefore be included as a full-fledged member in the
SM catalog of elementary particles.

Writing
in 1943, renowned Austrian physicist Edwin Schrodinger asked “What is Life?”
thereby invigorating the debate which preoccupied biologists at the time. He
proposed an answer to this question rooted in considerations borrowed from
Thermodynamics and Statistical Mechanics. To reveal the missing link in Biology-Physics,
the present Note investigates an alternate answer in which dynamical action,
rather than thermodynamics and energy, plays the fundamental role. It reviews
in particular the process of biological cell replication which may be
considered to define “Life” and might be the macroscopic manifestation of an
underlying quantum physical process in which xons, conveyors of dynamical
action, are the determining agents.

Abstract:
Using powerful
concepts and tools borrowed from the seminal arsenal connecting physics fundamentals
with esoteric set theoretical operations developed in recent years by Alexandria
E-infinity theoretician M. S. El Naschie, this paper explores the deep implications
of some of the dualities Dr El Naschie has identified and analyzed in his exposes,
connecting them with our own Xonic Quantum Physics (XQP) which places dynamical
action rather than spacetime and energy at the core of the System of the World.

Abstract:
As defined and used in General Relativity calculations, spacetime is a
strictly classical construct which
does not incorporate in any way, shape or form the concept of quantum. While reviewing the efforts that
Alexandria theoretician M. S. El Naschie has made to resolve the dichotomy, we discovered
that his E infinity theory contains a
Cantor set which has characteristics specified by Isaac Newton for Absolute
space. We show that this unexpected connection leads to an understanding of the
mysterious origin of the one and only attribute that all particles listed in
the Standard Model of Elementary Particles possess—including notably the photon—and
which has remained unexplained hitherto: spin. This most rewarding
result reinforces our belief in the relevance of the E infinity basic concepts in relation to our own Xonic Quantum
Physics (XQP) which places dynamical action rather spacetime and energy at the
core of the System of the World.

Abstract:
We extemporaneously summarize the theoretical scheme we have introduced recently in this note to account for the (hidden) functioning of the System of the World at the quantum level. We further explore the relevance, the pertinence and the potential validity of this scheme. We obtain new fundamental results, bearing notably on the nature and the origin of the “virtual particles” conventionally called upon in quantum field theories to explain the Casimir Effect. We define the concept of quantum meteorites in this context. We disable the Heisenberg Uncertainty Principle, judged to be a (mis) interpretation of otherwise legitimate observations, and we replace it with our new XQP Absolute Certainty Principle.

Abstract:
We retrieve three mysterious sentences Albert Einstein wrote in the early years of his wondrous scientific career. We examine their implications and we suggest that they provide a surprising new basis for Quantum Physics as well as some enlightenment concerning the whereabouts of Dark energy.

Abstract:
We resurrect the 1896 paper in the frame of which the great Swedish physical chemist Svante August Arrhenius explains why what he called “aqueous vapour” and “carbonic acid” should be regarded as determining climate warming agents. We suggest that the designation “Green House Effect Gas” as applied to carbon dioxide should be officially banished from the climate vocabulary as being misleading.