The worldwide
increase of the publications concerning the assessment of marine renewable
living resources is highlighting long-standing problems with symbols and
annotations. Starting from the symbols presented within the classic
fisheries masterpieces produced, mainly in the fifty of the last century, a
first “Milestone” list was organised. Thereafter, the pertinent literature
was (not exhaustively) browsed in order to integrate this Milestone list on the
base of a set of decisional criteria. The present contribution consists in
using the Latin letters as well established symbols for the corresponding parameters,
leaving free to specific use (with few historical exceptions) the Greek letters
in view to open a discussion among all the fisheries scientists and bodies in
order to move towards a common language and better communication standards.

Abstract:
In this paper, we study the k–Lucas numbers of arithmetic indexes of the form an+r , where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly the sums of the first k-Lucas numbers, and then for the even and the odd k-Lucas numbers. Later, we find the generating function of these numbers. Below we prove these same formulas for the alternated k-Lucas numbers. Then, we prove a relation between the k–Fibonacci numbers of indexes of the form 2rn and the k–Lucas numbers of indexes multiple of 4. Finally, we find a formula for the sum of the square of the k-Fibonacci even numbers by mean of the k–Lucas numbers.

The
atmospheric behaviour of air is largely governed by low and high pressure
systems. However, the relationship between these systems is not linear, as
winds, sea temperatures and solar intensity modulate their dynamics and reduce
predictability. Several other factors are known to affect these atmospheric
dynamics, such as solar cycles. Recent evidence shows however that the earth’s
gravitational field can be quantized in terms of quantum numbers, as recently
published in Nature. The implications of this relationship between gravity and
quantum numbers give rise to the possible key role of a quantum behaviour of
gravity in affecting the formation of high- and low-pressure systems. In this
letter, the author suggests a relation between the recently observed quantized
nature of gravity, the weight of air and the formation of Low and High pressure
areas in the atmosphere. The theory is novel and can aid in the understanding
of interplay between the earths core forces, the gravitational behaviour and
the atmospheric dynamics. There are however several parts of this theory that
need further development, and an initial expression of this putative
relationship is introduced.

Abstract:
In this paper, we will see that
some k -Fibonacci sequences
are related to the classical Fibonacci sequence of such way that we can express the terms of a k -Fibonacci sequence in function of some terms of the
classical Fibonacci sequence. And the formulas will
apply to any sequence of a certain set of k' -Fibonacci sequences. Thus we find k -Fibonacci sequences relating to other k -Fibonacci sequences when σ'_{k} is linearly dependent of .

Proposed here is a new framework for the analysis of
complex systems as a non-explicitly programmed mathematical hierarchy of
subsystems using only the fundamental principle of causality, the mathematics
of groupoid symmetries, and a basic causal metric needed to support measurement
in Physics. The complex system is described as a discrete set S of state variables. Causality is
described by an acyclic partial order w on S, and is considered as a
constraint on the set of allowed state transitions. Causal set (S, w)
is the mathematical model of the system. The dynamics it describes is
uncertain. Consequently, we focus on invariants, particularly group-theoretical
block systems. The symmetry of S by
itself is characterized by its symmetric group, which generates a trivial block
system over S. The constraint of
causality breaks this symmetry and degrades it to that of a groupoid, which may
yield a non-trivial block system on S.
In addition, partial order w determines a partial order for the blocks, and the set of blocks becomes a
causal set with its own, smaller block system. Recursion yields a multilevel
hierarchy of invariant blocks over S with the properties of a scale-free mathematical fractal. This is the invariant
being sought. The finding hints at a deep connection between the principle of
causality and a class of poorly understood phenomena characterized by the
formation of hierarchies of patterns, such as emergence, selforganization, adaptation, intelligence, and semantics.
The theory and a thought experiment are discussed and previous evidence is
referenced. Several predictions in the human brain are confirmed with wide
experimental bases. Applications are anticipated in many disciplines, including
Biology, Neuroscience, Computation, Artificial Intelligence, and areas of
Engineering such as system autonomy, robotics, systems integration, and image
and voice recognition.

Abstract:
This study presents an axisymmetric solution of the Einstein equations for empty space. The geometry is studied by determining its Petrov classification and killing vectors. Light propagation, orbital motion and asymptotic and Newtonian limits are also studied. Additionally, cosmological applications of the geometry are also outlined as an alternative model for the inflationary universe and as a substitute for dark matter and quintessence.

Abstract:
The big problem of Big Data is the lack of a machine learning process that scales and finds meaningful features. Humans fill in for the insufficient automation, but the complexity of the tasks outpaces the human mind’s capacity to comprehend the data. Heuristic partition methods may help but still need humans to adjust the parameters. The same problems exist in many other disciplines and technologies that depend on Big Data or Machine Learning. Proposed here is a fractal groupoid-theoretical method that recursively partitions the problem and requires no heuristics or human intervention. It takes two steps. First, make explicit the fundamental causal nature of information in the physical world by encoding it as a causal set. Second, construct a functor F: C C′ on the category of causal sets that morphs causal set C into smaller causal set C′ by partitioning C into a set of invariant groupoid-theoretical blocks. Repeating the construction, there arises a sequence of progressively smaller causal sets C, C′, C″, … The sequence defines a fractal hierarchy of features, with the features being invariant and hence endowed with a physical meaning, and the hierarchy being scale-free and hence ensuring proper scaling at all granularities. Fractals exist in nature nearly everywhere and at all physical scales, and invariants have long been known to be meaningful to us. The theory is also of interest for NP-hard combinatorial problems that can be expressed as a causal set, such as the Traveling Salesman problem. The recursive groupoid partition promoted by functor F works against their combinatorial complexity and appears to allow a low-order polynomial solution. A true test of this property requires special hardware, not yet available. However, as a proof of concept, a suite of sequential, non-heuristic algorithms were developed and used to solve a real-world 120-city problem of TSP on a personal computer. The results are reported.

Abstract:
Organizing in groups does not represent an objective definition, but rather a way to better understand the mean-ing of plurality. At the same time modern technologies modify perceptive and cognitive transformation. This re-search shows that on-line groups develop objective dynamics in face-to-face groups; it evaluates the quality of the University student services and studies the dynamics of the creation of face-to-face and on-line groups. Stu-dents were divided into experimental on-line (forum, chat, newsgroup) and face-to-face encounters (seminars, laboratories). The two level analyses show the defence mechanisms, the lack of socialization attitudes and the tolerance of differences that characterized on-line groups. The new technologies open new horizons and cogni-tive functions.

Abstract:
In this paper we study stochastic dominance rules of first and second order for univariate skew-normal random variables, the analysis being relevant in connection with the problem of portfolio choice in stock markets showing departure from the classical assumption of normality on returns. Besides that, our analysis is also relevant for markets where stocks returns are normally distributed: if standard derivatives are tradable and straddles, characterized by V-shaped pay-outs, are implementable at specific strike prices, then, portfolios including them, can exhibit exact skew-normality in their returns. We provide a set of simple conditions on the statistical parameters of the distributions which imply FSD and SSD and discuss some application of our criteria.

Abstract:
A straightforward
conceptual method is proposed to quantitatively assess the seasonal-scale
tendency of retreatment or advancement on microtidal beaches by using the
backshore/foreshore length ratio. This method is based on measuring the
cross-shore profile of a beach when it passes through the “transitional state”
that separates the high-from the low-energy season, period during which the
morphological characteristics of the beach tend to its equilibrium profile. In
order to obtain real measurements of backshore (B) and foreshore (F),
the definition of the limits bounding these two important components in
subaerial beaches is reviewed and discussed. The approach based on the
measurement of theB/Flength ratio assumes that foreshore
and backshore have equivalent lengths in beaches that approximate to their
state of morphodynamic equilibrium (B/F~
1). A backshore length exceeding the foreshore length is indicative of a state
of beach recession, with aB/Flength ratio > 1. When the
foreshore length is greater than the backshore length, the shoreline is
advancing or, alternatively, it is developing in a state of morphological
confinement,i.e.due to the