Typography: the constant vector of dynamic logos

Visual identities can be constructed from a number of elements which together can be described as the Visual Identity System (VIS). Typography is one of the VIS’s central elements. Typically, the VIS elements have been considered as static and associated with prescribable visual mandates; however, the hypermodernity paradigm boosted the notion of mobility in everything – and brands are no exception. Brand logos now change in shape, colour, wear different textures and sit on top of a variety of backgrounds. All this incredible flexibility has implications for their typographical elements too. In the empirical part of this research, 50 dynamic logos were selected, grouped according to Van Nes’ categories in Dynamic Identities: How to Create a Living Brand (2012) and the changes in their typographic components were analysed under the Multilingual Typeface Anatomy Terminology framework (Amado, 2012), firstly by the researchers, and then by a group of independent coders. It was verified that dynamic logos present a consistent pattern regarding typography since they preserve consistency through type’s structural axes. This result led to a set of recommendations for both designers working with type in the context of the (re)design of dynamic logos, and academics preparing the next generation of brand designers. This research aimed at identifying the typographical inroads in brands with dynamic logos and is a relevant contribution to the perception of how the anatomy of type can define visual consistency.

Lorentz symmetry breaking in supersymmetric quantum electrodynamics

Lorentz symmetry is one of the fundamental symmetries of nature; however, it can be broken by several proposals such as quantum gravity effects, low energy approximations in string theory and dark matter. In this paper, Lorentz symmetry is broken in supersymmetric quantum electrodynamics using aether superspace formalism without breaking any supersymmetry. To break the Lorentz symmetry in three-dimensional quantum electrodynamics, we must use the [Formula: see text] aether superspace. A new constant vector field is introduced and used to deform the deformed generator of supersymmetry. This formalism is required to fix the unphysical degrees of freedom that arise from the quantum gauge transformation required to quantize this theory. By using Yokoyama’s gaugeon formalism, it is possible to study these gaugeon transformations. As a result of the quantum gauge transformation, the supersymmetric algebra gets modified and the theory is invariant under BRST symmetry. These results could aid in the construction of the Gravity’s Rainbow theory and in the study of superconformal field theory. Furthermore, it is demonstrated that different gauges in this deformed supersymmetric quantum electrodynamics can be related to each other using the gaugeon formalism.

Multi-GGS Groups have the Congruence Subgroup Property

We generalize the result about the congruence subgroup property for GGS groups in [3] to the family of multi-GGS groups; that is, all multi-GGS groups except the one defined by the constant vector have the congruence subgroup property. New arguments are provided to produce this more general proof.

Hypersurfaces with Generalized 1-Type Gauss Maps

In this paper, we study submanifolds in a Euclidean space with a generalized 1-type Gauss map. The Gauss map, G, of a submanifold in the n-dimensional Euclidean space, En, is said to be of generalized 1-type if, for the Laplace operator, Δ, on the submanifold, it satisfies ΔG=fG+gC, where C is a constant vector and f and g are some functions. The notion of a generalized 1-type Gauss map is a generalization of both a 1-type Gauss map and a pointwise 1-type Gauss map. With the new definition, first of all, we classify conical surfaces with a generalized 1-type Gauss map in E3. Second, we show that the Gauss map of any cylindrical surface in E3 is of the generalized 1-type. Third, we prove that there are no tangent developable surfaces with generalized 1-type Gauss maps in E3, except planes. Finally, we show that cylindrical hypersurfaces in En+2 always have generalized 1-type Gauss maps.

Rotational hypersurfaces with $L_r$-pointwise 1-type Gauss map

In this paper, we study hypersurfaces in $\E^{n+1}$ which Gauss map $G$ satisfies the equation $L_rG = f(G + C)$ for a smooth function $f$ and a constant vector $C$, where $L_r$ is the linearized operator of the $(r + 1)$th mean curvature of the hypersurface, i.e., $L_r(f)=tr(P_r\circ\nabla^2f)$ for $f\in \mathcal{C}^\infty(M)$, where $P_r$ is the $r$th Newton transformation, $\nabla^2f$ is the Hessian of $f$, $L_rG=(L_rG_1,\ldots,L_rG_{n+1}), G=(G_1,\ldots,G_{n+1})$. We show that a rational hypersurface of revolution in a Euclidean space $\E^{n+1}$ has $L_r$-pointwise 1-type Gauss map of the second kind if and only if it is a right n-cone.

A note on proper curvature symmetry in general cylindrically symmetric four-dimensional Lorentzian manifolds

We considered the most general form of non-static cylindrically symmetric space-times for studying proper curvature symmetry by using the rank of the [Formula: see text] Riemann matrix and direct integration techniques. Studying proper curvature symmetry in each case of the above space-times, we show that when the above space-times admit proper curvature symmetry, they form an infinite dimensional vector space. It is important to note that here we also find the case when the rank of the [Formula: see text] Riemann matrix is one and no covariantly constant vector fields exist.

Generalized null 2-type immersions in Euclidean space

We define generalized null 2-type submanifolds in them-dimensional Euclidean space 𝔼m. Generalized null 2-type submanifolds are a generalization of null 2-type submanifolds defined by B.-Y. Chen satisfying the conditionΔ H=f H+gCfor some smooth functionsf,gand a constant vectorCin 𝔼m, whereΔandHdenote the Laplace operator and the mean curvature vector of a submanifold, respectively. We study developable surfaces in 𝔼3and investigate developable surfaces of generalized null 2-type surfaces. As a result, all cylindrical surfaces are proved to be of generalized null 2-type. Also, we show that planes are the only tangent developable surfaces which are of generalized null 2-type. Finally, we characterize generalized null 2-type conical surfaces.

Asymptotic method for solution of identification problem of the nonlinear dynamic systems

A dynamic system, when the motion of the object is described by the system of nonlinear ordinary differential equations, is considered. The right part of the system involves the phase coordinates as a unknown constant vector-parameter and a small number. The statistical data are taken from practice: the initial and final values of the object coordinates. Using the method of quasilinearization the given equation is reduced to the system of linear differential equations, where the coefficients of the coordinate and unknown parameter, also of the perturbations depend on a small parameter linearly. Then, by using the least-squares method the unknown constant vector-parameter is searched in the form of power series on a small parameter and for the coefficients of zero and the first orders the analytical formulas are given. The fundamental matrices both in a zero and in the first approach are constructed approximately, by means of the ordinary Euler method. On an example the determination of the coefficient of hydraulic resistance (CHR) in the lift in the oil extraction by gas lift method is illustrated, as the obtained results in the first approaching coincides with well-known results on order of 10-2.

The Divergence Equation

This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a smooth function and a smooth vector field on ³, plus an unknown, symmetric (2, 0) tensor. The chapter presents a proposition that takes into account a condition relating to the conservation of momentum as well as a condition that reflects Newton's law, which states that every action must have an equal and opposite reaction. This axiom, in turn, implies the conservation of momentum in classical mechanics. In view of Noether's theorem, the constant vector fields which act as Galilean symmetries of the Euler equation are responsible for the conservation of momentum. The chapter shows proof that all solutions to the Euler-Reynolds equations conserve momentum.