On the Accuracy of a Stewart Platform: Modelling and Experimental Validation

Non

Pilot Aquaponic Growing System of Carp (Cyprinus Carpio) and Basil (Ocimum Basilicum)

AbstractThe aquaponic recirculating systems are integrated systems that combine fish and plant culture. These systems consist of two components: aquaculture and hydroponics components. In these systems the nutrients necessary for plant growth are resulted from the metabolism of food by the fish. This was obtained by recirculation of water, with a pump, from the fish tank to the hydroponic component and back to the fish tank. The experiment was conducted in the laboratory of Fisheries and Aquaculture of the Faculty of Animal Husbandry of University of Agronomic Sciences and Veterinary Medicine of Bucharest for 6 months. The system developed here, is a 1 m2 area of plant growth and 0.45 m3 of water in aquaculture component. In the hydroponic component river gravel was selected to support the plants and offer support for the growth and developing of nitrifying bacteria. The species cultivated were cultured carp (Cyprinus carpio) and basil (Ocimum basilicum). On average, there was obtained a quantity of about 1kg basil leaves in a period of 60 days of growth. It has been found that the species of plants grown in this system, namely basil (Ocimum basilicum) grown with carp (Cyprinus carpio), has a faster and better development compared to conventional growth. Use of basil as a purifying plant, resulted in the removal of nitrates, being not necessary to add additional water, as in classical recirculating systems, where is necessary to replace daily approx. 10% of the volume of the culture water being necessary to add into the system only water lost through evaporation. According to the results the basil is suitable for aquaponic system with carp culture. The basil was grown much better than the conventional cultivation

A new foundational crisis in mathematics, is it really happening?

The article reconsiders the position of the foundations of mathematics after the discovery of HoTT. Discussion that this discovery has generated in the community of mathematicians, philosophers and computer scientists might indicate a new crisis in the foundation of mathematics. By examining the mathematical facts behind HoTT and their relation with the existing foundations, we conclude that the present crisis is not one. We reiterate a pluralist vision of the foundations of mathematics. The article contains a short survey of the mathematical and historical background needed to understand the main tenets of the foundational issues.Comment: Final versio

Holomorphic potentials for graded D-branes

We discuss gauge-fixing, propagators and effective potentials for topological A-brane composites in Calabi-Yau compactifications. This allows for the construction of a holomorphic potential describing the low-energy dynamics of such systems, which generalizes the superpotentials known from the ungraded case. Upon using results of homotopy algebra, we show that the string field and low energy descriptions of the moduli space agree, and that the deformations of such backgrounds are described by a certain extended version of `off-shell Massey products' associated with flat graded superbundles. As examples, we consider a class of graded D-brane pairs of unit relative grade. Upon computing the holomorphic potential, we study their moduli space of composites. In particular, we give a general proof that such pairs can form acyclic condensates, and, for a particular case, show that another branch of their moduli space describes condensation of a two-form.Comment: 47 pages, 7 figure

Codimension-3 Singularities and Yukawa Couplings in F-theory

F-theory is one of the frameworks where all the Yukawa couplings of grand unified theories are generated and their computation is possible. The Yukawa couplings of charged matter multiplets are supposed to be generated around codimension-3 singularity points of a base complex 3-fold, and that has been confirmed for the simplest type of codimension-3 singularities in recent studies. However, the geometry of F-theory compactifications is much more complicated. For a generic F-theory compactification, such issues as flux configuration around the codimension-3 singularities, field-theory formulation of the local geometry and behavior of zero-mode wavefunctions have virtually never been addressed before. We address all these issues in this article, and further discuss nature of Yukawa couplings generated at such singularities. In order to calculate the Yukawa couplings of low-energy effective theory, however, the local descriptions of wavefunctions on complex surfaces and a global characterization of zero-modes over a complex curve have to be combined together. We found the relation between them by re-examining how chiral charged matters are characterized in F-theory compactification. An intrinsic definition of spectral surfaces in F-theory turns out to be the key concept. As a biproduct, we found a new way to understand the Heterotic--F theory duality, which improves the precision of existing duality map associated with codimension-3 singularities.Comment: 91 pages; minor clarification, typos corrected and a reference added (v3

Gauge-fixing, semiclassical approximation and potentials for graded Chern-Simons theories

We perform the Batalin-Vilkovisky analysis of gauge-fixing for graded Chern-Simons theories. Upon constructing an appropriate gauge-fixing fermion, we implement a Landau-type constraint, finding a simple form of the gauge-fixed action. This allows us to extract the associated Feynman rules taking into account the role of ghosts and antighosts. Our gauge-fixing procedure allows for zero-modes, hence is not limited to the acyclic case. We also discuss the semiclassical approximation and the effective potential for massless modes, thereby justifying some of our previous constructions in the Batalin-Vilkovisky approach.Comment: 46 pages, 4 figure

T-duality and Actions for Non-Commutative D-Branes

We show how the T-duality is realized for D-branes with noncommutative world-volume coordinates. We discuss D-branes wrapped on tori and the result is that the recently found noncommutative actions form a consistent collection due to the T-duality mapping between noncommutative D-branes and rotated commutative D-branes on deformed tori.Comment: Latex, 11 page

Proton Decay, Yukawa Couplings and Underlying Gauge Symmetry in String Theory

In string theory, massless particles often originate from a symmetry breaking of a large gauge symmetry G to its subgroup H. The absence of dimension-4 proton decay in supersymmetric theories suggests that (\bar{D},L) are different from \bar{H}(\bar{\bf 5}) in their origins. In this article, we consider a possibility that they come from different irreducible components in $\mathfrak{g}/\mathfrak{h}$. Requiring that all the Yukawa coupling constants of quarks and leptons be generated from the super Yang--Mills interactions of G, we found in the context of Georgi--Glashow H=SU(5) unification that the minimal choice of G is E_7 and E_8 is the only alternative. This idea is systematically implemented in Heterotic String, M theory and F theory, confirming the absence of dimension 4 proton decay operators. Not only H=SU(5) but also G constrain operators of effective field theories, providing non-trivial information.Comment: 73 page

1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --

We systematically classify 1/2, 1/4 and 1/8 BPS equations in SUSY gauge theories in d=6, 5, 4, 3 and 2 with eight supercharges, with gauge groups and matter contents being arbitrary. Instantons (strings) and vortices (3-branes) are only allowed 1/2 BPS solitons in d=6 with N=1 SUSY. We find two 1/4 BPS equations and the unique 1/8 BPS equation in d=6 by considering configurations made of these field theory branes. All known BPS equations are rederived while several new 1/4 and 1/8 BPS equations are found in dimension less than six by dimensional reductions.Comment: 41 pages, no figures, v2: 49 pages, no figures, typos corrected, references added, the final version in NP

Right-handed Neutrinos in F-theory Compactifications

F-theory is one of the frameworks where up-type Yukawa couplings of SU(5) unified theories are naturally generated. As charged matter fields have localized zero modes in F-theory, a study of flavor structure could be easier in F-theory than in Heterotic string theory. In a study of flavor structure in the lepton sector, however, an important role is played by right-handed neutrinos, which are not charged under the SU(5) unified gauge group. It is therefore solicited to find out what right-handed neutrinos are in F-theory compactifications and how their Majorana mass terms are generated together with developing a theoretical framework where effective Yukawa couplings involving both SU(5)-neutral and charged fields can be calculated. We find that the complex structure moduli chiral multiplets of F-theory compactifications are good candidates to be right-handed neutrinos, and that their Majorana masses are automatically generated in flux compactifications. The mass scale is predicted to be somewhat below the GUT scale, which is in nice agreement with the Delta m^2 of the atmospheric neutrino oscillation through the see-saw mechanism. We also discuss various scenarios of solving the dimension-4 proton decay problem in supersymmetric F-theory compactifications, along with considering the consequences of those scenarios in the nature of right-handed neutrinos.Comment: 61 page