Complex Numbers for Relativistic Operations

When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.

Characterization of Odontoblasts in Supernumerary Tooth-derived Dental Pulp Stem Cells between Passages by Real-Time PCR

The aim of this study is to compare the properties of odontoblast gene of early passage cells and late passage cells derived from impacted maxillary supernumerary teeth. Impacted supernumerary teeth with maxilla were extracted from 12 patients (8 males, 4 females) between 6 - 9 years old without medical history. Real-time polymerase chain reaction (PCR) was conducted to compare characterization of odontoblast cell in the 3rd and 10th passage, and between with bone inducing additive group and without additive group. Genes for odontoblasts characteristics are osteonectin (ONT), alkaline phosphatase (ALP), osteocalcin (OCN), dentin matrix protein 1 (DMP-1) and dentin sialophosphoprotein (DSPP). The level of gene expression was in a decreasing order of ONT, ALP, OCN, DMP-1 and DSPP in the 3rd passage, and in decreasing order of ONT, DMP-1, OCN, ALP, and DSPP in the 10th passage in the undifferentiation and differentiation group. The order of ONT, DMP-1, and OCN did not changed. ALP and DMP-1 were switched in order. ALP and DMP-1 may be used as important markers for differentiating between the 3rd passage and 10th passage cells. Considering that supernumerary tooth was extracted young age and the time required to cultured 10th passage was short, supernumerary tooth can be considered a useful donor site of dental pulp stem cells.

Solvability of the control problem of the asynchronous spectrum of linear almost periodic systems with a lower triangular representation of the averaging of coefficient matrix

A linear control system with an almost periodic matrix of coefficients and control in the form of the feedback linear in phase variables is considered. It is assumed that the feedback coefficient is almost periodic and its frequency module, i. e. the smallest additive group of real numbers, including all the Fourier exponents of this coefficient, is contained in the frequency module of the coefficient matrix. The system under consideration is studied in the case of a triangular average value of the matrix of coefficients. For the described class of systems, the control problem of the asynchronous spectrum with a target set of frequencies is solved. This task is to construct such a control from an admissible set that the system closed by this control has almost periodic solutions, a set of the Fourier exponents of which contains a predetermined subset, and the intersection of the solution frequency modules and the coefficient matrix is trivial. The necessary and sufficient conditions for the solvability of this problem are obtained.

Effects of JGB Additives on the Microstructures and Electrical Properties of Electroplated Copper Foil

Extremely thin film high quality copper foil is required to ensure high performance in electronics and slimness in secondary batteries. During the electroplating of copper foil, Janus Green B(JGB) and Collagen were introduced as additives to the electrolytes to study their effects. The structural and electrical properties of the electroplated copper foil were evaluated. When each additive was added individually, the potential was increased. Specifically, the potential of the group with 30 ppm added collagen was about 27% higher rather than the non-additive group. When Cl- ions and MPSA(3-mercapto-1-propane sulfonic acid) were added to the electrolytes without collagen and JGB, the surface roughness(Rz) increased by about 136% to 2.24 μm compared to the non-additive group. This was the highest value among all groups. However, a uniform layer with a surface roughness value below 0.3 μm was formed when less than 30 ppm and 10 ppm collagen and JGB were added, respectively, to the electrolyte. The direction of crystal growth with the JGB additives tended to go forward to the (220) direction, and the crystal size was reduced by 10~27% compared to the non-additive group. The addition of Collagen is necessary to reduce the difference in resistivity of the shiny layer and right matte layer. JGB additives were required to reduce the deviation in grain size. The results confirmed that the accelerators, inhibitors and leveler need to be properly added to form a copper plating layer with low surface roughness and to reduce differences in crystal texture of the shiny layer and right matte layer. Copper foil can be safely and uniformly deposited from electrolytes with JGB below 10 ppm and collagen below 30 ppm.

Actions of the additive group Ga on certain noncommutative deformations of the plane

We connect the theorems of Rentschler [18] and Dixmier [10] on locally nilpotent derivations and automorphisms of the polynomial ring A 0 and of the Weyl algebra A 1, both over a field of characteristic zero, by establishing the same type of results for the family of algebras A h = 〈 x , y | y x − x y = h ( x ) 〉 , {A_h} = \left\langle {x,y|yx - xy = h\left( x \right)} \right\rangle , , where h is an arbitrary polynomial in x. In the second part of the paper we consider a field 𝔽 of prime characteristic and study 𝔽[t]-comodule algebra structures on Ah . We also compute the Makar-Limanov invariant of absolute constants of Ah over a field of arbitrary characteristic and show how this subalgebra determines the automorphism group of Ah .

Initial Behavior of Additives and Mechanical Properties of Copper Foils on High Current Density

In this study, we studied the surface and mechanical properties of multiple additives as well as the initial plating properties of individual additives. With the individual additive groups, copper crystals tended to converge at a stage above the critical amount of additive. When chloride ions were added, large crystals formed at several places on the surface. Thereafter, small crystals were attached to and grew on the surface of the large crystals. When collagen and JGB (Janes Green B) were added individually, the crystals were more uniformly distributed on the surface as compared with the group with added chloride ions. In addition, starlike crystals were grown depending on the amount of addition. It was necessary to use multiple additives, which is why it is difficult to make a uniform surface layer with individual additives. Large crystals of more than 10 μm formed unevenly on the surface treated with multiple additives of chloride ions and MPSA (3-mercapto-1-propane sulfonic acid). Large crystals disappeared on the surface treated with additional collagen along with multiple additives. However, valley like shapes were observed on this surface, due to the large crystals. But, addition of JGB additives to this reduced the valley and formed a uniform plating layer. MPSA and 20 ppm of collagen were added as multiple additives, grain sizes increased by 93.5% (220 peak) and 172.3% (311 peak) compared with the non-additive group. As a result, tensile strength decreased by 24.5% and elongation increased by 17.8%. The crystal size was reduced 25.0% on average by the addition of 10 ppm JGB, which contributed to a 5.4% increase in tensile strength and a 16.0% decrease in elongation. The grain size and surface properties could be controlled by adding multiple combinations of additives. As a result, It was confirmed that mechanical properties could be controlled by the proper amount and the optimum combination of additives.