Inner Product Research Articles

Inner product of RGB unit vectors for detecting color transition: application to feedback-based flow ratiometric titration.

The inner product (IP) of RGB unit vectors' approach for detecting color transition has further been applied to a feedback-based flow ratiometric titration, including nonaqueous titration. While the flow ratio of titrand/titrant containing an indicator was varying, the video image of the merged solution was taken with a digital microscope downstream. The indicator's color was converted to an RGB unit vector. The change in IP between vectors was used for determining the equivalence point. The concept was successfully applied to the determinations of drug and vinegar samples with reasonable throughput rate (> 18s/titration) and precision (RSD < 4.4%).

On the Bohr and Selberg inequalities in 2-*-inner product spaces

The Bohr inequality occurs for scalars, vectors, matrices and operators. In this paper, we introduce the new type of Bohr's inequality in Hilbert -modules and in 2--inner product spaces, which is equipped by a 2-inner product map that takes values on locally -algebras. Then, we obtain a version of the Selberg and Bessel inequality and its results in an -2-inner product space.

Data-Induced Rationality and Unitary Spaces in Interfirm Collaboration

The real-time data transfer between collaborating companies allows them to represent and control activities across firm boundaries, providing new ways to organize collaborative efforts. We conducted an inductive multiple case study of five long-term relationships to examine the effects of data-intensive technologies on the organization and management of collaborative relationships in industrial companies. Our analysis shows how the delegation of digital activities into specialized digital units fostered data-driven mindsets and data-driven interactions that jointly formed a holistic data-induced rationality for managing the relationship. Together, the compartmentalization of digital collaboration and the data-induced rationalities turned these units into “unitary spaces,” organizational enclosures where structural tensions and competing demands were temporarily suspended to foster single-minded pursuit of collaborative short-term benefits for the partner company. Funding: The authors are grateful for the financial support from the Academy of Finland [Grant 274536].

Characterization of inner product spaces by unitary Carlsson type orthogonalities

In this study, we consider the Hermite-Hadamard type of unitary Carlsson?s orthogonality (UHH-C-orthogonality) to characterize real inner product spaces. We give a necessary and sufficient condition weaker than the homogeneity of symmetric HH-C-orthogonalities which characterizes inner product spaces among normed linear spaces of dimension at least three. In conclusion, some more characterizations of real inner product spaces are provided.

АЛГЕБРАИЧЕСКИЕ УРАВНЕНИЯ В УНИТАРНОМ ПРОСТРАНСТВЕ И КРАТЧАЙШЕЕ АЛГЕБРАИЧЕСКОЕ ДОКАЗАТЕЛЬСТВО ОСНОВНОЙ ТЕОРЕМЫ АЛГЕБРЫ

The article deals with the presentation of some results obtained in the study of algebraic equations with complex coefficients from a complex variable in a unitary space. In the orthonormal basis, two vectors are introduced, which are called the vector of root and the vector of coefficients of an algebraic polynomial. With the help of these vectors, an algebraic polynomial is represented as a scalar product of them in an orthonormal basis. The criterion of linear independence of a set of root vectors is formulated and proved. A Theorem is formulated and proved that the maximum number of simple roots of an algebraic polynomial is one less than the dimension of a unitary space. A generalization of Vieta’s Theorem is obtained and new formulas connecting the coefficients of an algebraic polynomial with its roots are derived. The general case of an algebraic polynomial is considered, when some of its coefficients may be equal to zero. Two orthogonal vector systems from combinations of coefficients of an algebraic polynomial are introduced. Their properties have been studied. The shortest algebraic proof of the fundamental Theorem of algebra among the known proofs is given, which does not go beyond the concepts of the algebra of polynomials and uses the scalar product of vectors in a unitary space, as well as one property of a two-place predicate from mathematical logic. The results of this work can also be used in the educational process in the algebra course.

Insulin Resistance and the Metabolic Syndrome severity – a mathematical model

Excessive fructose consumption was shown to have deleterious effects on the cardiovascular system, particularly as the metabolic syndrome. However, the degree by which alteration of each pathophysiological factor contributes to the morbidity associated with fructose consumption is not yet clear. We have developed a mathematical model to integrate and uniformly quantify pathophysiological features of the metabolic syndrome on a high fructose-fed dog model. A novel comprehensive measure for the syndrome severity (the “patholog”) and a more intuitive measure of the insulin resistance are introduced. Alteration of hemodynamics, echocardiography and blood chemistry were determined in adult male mongrel dogs fed with 60% isocaloric fructose or normal chow for 7 weeks. The diverse experimental data were transformed into comparable scores and a pre-Hilbert space of states constructed. In such a space one can quantify the severity of any combination of pathophysiological and genomic features and determine the global recovery resulting from a treatment. The model indicates increase of insulin resistance (new index proposed), systolic blood pressure, low-to-high density lipids ratio and angiotensin II as the major contributors to the excessive fructose morbidity. Our model provides the simplest, yet the most intuitive and comprehensive way to integrate data of a wide diversity in visualizing and quantifying a cardiovascular disease

The filmic space of the Overlook Hotel in the Shining through the sets

AbstractFor the construction of the Overlook Hotel (The Shining, 1980) Stanley Kubrick recreates, at Elstree Studios in London, 1:1 scale replicas of different fragments of hotels, motels, and vacation resorts scattered throughout the United States. Through a meticulous work of observing photographs and making models, sets of the different areas that make up the hotel are built. Kubrick composes an architecture that emerges from a fragmentary, constructed and assembled body which, through the narrative possibilities offered by the Steadicam and montage, is transformed into a seemingly unitary filmic space. The hotel is rendered as a plausible architecture; however, it is full of paradoxes, external references, subtexts, and spatial impossibilities—which emerge with an attentive viewing of the film—through a persistent subversion of the logics of space. Using models, photographs, and interviews, and comparing them with the film, plans of the different areas of the Overlook Hotel are drawn up with the aim of reflecting on the intention of their possible assembly. They are also drawn with the aim of reflecting on the existing link between the narrative structure of the film, based on intertwining times and spaces, and the way in which the sets come together on screen. Through an analysis based on architectural expression, the article will study some of these spatial inconsistencies to speculate on a possible interpretation of the film in which architecture plays a central role from its conception, not only due to the importance of its sets during the production and filming stages, but also on an iconographic and narrative level.

Parameterizing qudit states

Quantum systems with a finite number of states at all times have been a primary element of many physical models in nuclear and elementary particle physics, as well as in condensed matter physics. Today, however, due to a practical demand in the area of developing quantum technologies, a whole set of novel tasks for improving our understanding of the structure of finite-dimensional quantum systems has appeared. In the present article we will concentrate on one aspect of such studies related to the problem of explicit parameterization of state space of an NN-level quantum system. More precisely, we will discuss the problem of a practical description of the unitary SU(N){SU(N)}-invariant counterpart of the NN-level state space BN{\mathcal{B}_N}, i.e., the unitary orbit space BN/SU(N){B_N/SU(N)}. It will be demonstrated that the combination of well-known methods of the polynomial invariant theory and convex geometry provides useful parameterization for the elements of BN/SU(N){B_N/SU(N)}. To illustrate the general situation, a detailed description ofBN/SU(N){B_N/SU(N)} for low-level systems: qubit (N=2{N= 2}), qutrit (N=3{N=3}), quatrit (N=4{N= 4}) - will be given.

Inner-product quasilinear spaces with applications in signal processing

If certain characteristics of a non-deterministic signal are known, can some approximate results be obtained concerning the frequency, deterministic autocorrelation or other characteristics of the signal? The mathematical techniques we have developed allow us to obtain some approximate estimations of this type. In this way we use some new mathematical methods so called quasilinear functional analysis. Interval analysis also in the scope of this area and we use complex interval-valued signals in calculations. Especially, in this work, we give some special properties and results of inner-product quasilinear spaces which are generalizations of classical inner-product spaces. By this results we give easy examples of approximate estimations of deterministic autocorrelation of some semi non-deterministic signals or signals with inexact data. Further, we have constructed the space $\mathbb{I}l_{2}$ and we have showed that $\mathbb{I}l_{2}$ is an inner-product quasilinear space. This space provides a basis for an estimation of deterministic autocorrelation of the signals with inexact data.

Induced operators on the generalized symmetry classes of tensors

‎Let $V$ be a unitary space‎. ‎Suppose $G$ is a subgroup of the symmetric group of degree $m$ and $Lambda$ is an irreducible unitary representation of $G$ over a vector space $U$‎. ‎Consider the generalized symmetrizer on the tensor space $Uotimes V^{otimes m}$‎, ‎$$ S_{Lambda}(uotimes v^{otimes})=dfrac{1}{|G|}sum_{sigmain G}Lambda(sigma)uotimes v_{sigma^{-1}(1)}otimescdotsotimes v_{sigma^{-1}(m)} $$ defined by $G$ and $Lambda$‎. ‎The image of $Uotimes V^{otimes m}$ under the map $S_Lambda$ is called the generalized symmetry class of tensors associated with $G$ and $Lambda$ and is denoted by $V_Lambda(G)$‎. ‎The elements in $V_Lambda(G)$ of the form $S_{Lambda}(uotimes v^{otimes})$ are called generalized decomposable tensors and are denoted by $ucircledast v^{circledast}$‎. ‎For any linear operator $T$ acting on $V$‎, ‎there is a unique induced operator $K_{Lambda}(T)$ acting on $V_{Lambda}(G)$ satisfying $$ K_{Lambda}(T)(uotimes v^{otimes})=ucircledast Tv_{1}circledast cdots circledast Tv_{m}‎. ‎$$ If $dim U=1$‎, ‎then $K_{Lambda}(T)$ reduces to $K_{lambda}(T)$‎, ‎induced operator on symmetry class of tensors $V_{lambda}(G)$‎. ‎In this paper‎, ‎the basic properties of the induced operator $K_{Lambda}(T)$ are studied‎. ‎Also some well-known results on the classical Schur functions will be extended to the case of generalized Schur functions‎.

Electromagnetic curves and Rytov curves based on the hyperbolic split quaternion algebra

This paper aims to investigate the hyperbolically the motion of the polarization plane traveling along the linearly polarized light wave in the optical fiber via the hyperbolic split quaternion algebra. The motion of the electric field (polarization vector) about an axis on the general hyperboloid is described by the Lorentzian scalar product space Ra1,a2,a32,1. The hyperbolic geometric (Berry) phase models are generated through the pseudo-spheres of Ra1,a2,a32,1. Then, the parametric representations of the Rytov curves are obtained via the hyperbolic split quaternion product and one-parameter homothetic motion. Then, the hyperbolically motion of the electric field is expressed by the Fermi–Walker parallel transportation law. Moreover, the electromagnetic curves (EM-curves) associated with the electric field E are determined via the hyperbolic geometric phase models in the optical fiber. Furthermore, some motivating examples are presented by using the MAPLE program.

Norms on Quotient Spaces of The 2-Inner Product Space

This paper discussed about construction of some quotients spaces of the 2-inner product spaces. On those quotient spaces, we defined an inner product with respect to a linear independent set. These inner products was derived from the -inner product. We then defined a norm which induced by the inner product in these quotient spaces.

On a certain class of positive definite functions and measures on locally compact Abelian groups and inner-product spaces

Let L be a lattice in Rn and φ the L-periodic Gaussian function on Rn given by φ(x)=∑y∈Le−‖x−y‖2. The paper was motivated by the following observation: φ(x+y)φ(x−y) is a positive definite function of two variables x,y. We say that a positive definite function φ on an Abelian group G is cross positive definite (c.p.d.) if, for each z∈G, the function φ(x+y+z)φ(x−y) of two variables x,y is positive definite. We say that a finite Radon measure on a locally compact Abelian group is c.p.d. if its Fourier transform is a c.p.d. function on the dual group. We investigate properties of c.p.d. functions and measures and give some integral characterizations. It is proved that the classes of c.p.d. functions and measures are closed with respect to certain natural operations. In particular, products, convolutions and Fourier transforms of c.p.d. functions and measures are c.p.d., whenever defined.

Violation of unitarity in gravitational subregions

This essay contends that in quantum gravity, some spatial regions do not admit a unitary Hilbert space. Because the gravitational path integral spontaneously breaks CPT symmetry, “states” with negative probability can be identified on either side of trapped surfaces. I argue that these negative norm states are tolerable, by analogy to quantum mechanics. This viewpoint suggests a resolution of the firewall paradox, similar to black hole complementarity. Implications for cosmology are briefly discussed.

An algorithm for verifying some norm identities in inner-product spaces

In this paper, we provide an algorithm for verifying the validity of identities of the form ∑A⊆n¯cA‖xA‖2=0, where xA=∑i∈Axi and n¯={1,⋯,n} in inner-product spaces. Such algorithm is used to verify the validity, in inner-product spaces, for a number of identities. These include a generalization of the parallelepiped law. We also show that such identities hold only in inner-product spaces. Thus, the algorithm can be used to deduce characterizations of inner-product spaces.

Merging familiar and new senses to perceive and act in space

Our experience of the world seems to unfold seamlessly in a unitary 3D space. For this to be possible, the brain has to merge many disparate cognitive representations and sensory inputs. How does it do so? I discuss work on two key combination problems: coordinating multiple frames of reference (e.g. egocentric and allocentric), and coordinating multiple sensory signals (e.g. visual and proprioceptive). I focus on two populations whose spatial processing we can observe at a crucial stage of being configured and optimised: children, whose spatial abilities are still developing significantly, and naïve adults learning new spatial skills, such as sensing distance using auditory cues. The work uses a model-based approach to compare participants’ behaviour with the predictions of alternative information processing models. This lets us see when and how—during development, and with experience—the perceptual-cognitive computations underpinning our experiences in space change. I discuss progress on understanding the limits of effective spatial computation for perception and action, and how lessons from the developing spatial cognitive system can inform approaches to augmenting human abilities with new sensory signals provided by technology.

PENGELOLAAN KEBERSIHAN DAN KESEHATAN LINGKUNGAN DI DESA SEMUT KECAMATAN WONOKERTO KABUPATEN PEKALONGAN

&lt;p&gt;The living environment is a unitary space with all objects, forces, conditions, and living things, including humans and their behavior that affect the continuity of life and the welfare of humans and other living creatures. Environmental awareness is an effort to grow and develop awareness of the environment which does not only include garbage, pollution, greening animal protection, but furthermore how people have a love for land and water to achieve justice, prosperity and environmental sustainability. This community service regarding the management of environmental hygiene and health is carried out in Semut Village, Wonokerto District, Pekalongan Regency with the target population of the village community. The purpose of this activity is to build a culture of environmental awareness and increase community participation in environmental hygiene and health. The results of the activity can run smoothly, as evidenced by the role of participants who follow from elements of the community, and more importantly the growing public awareness of the importance of protecting the environment which includes cleanliness and environmental awareness, and increasing public understanding and awareness about environmental hygiene and health. Assistance activities to the community by involving all related components from the village, sub-district, and related offices in Pekalongan Regency can be carried out to maintain the continuity of these activities.&lt;/p&gt;&lt;strong&gt;Keywords&lt;/strong&gt;: Village, &lt;em&gt;environment, environmental awareness, cleanliness, health&lt;/em&gt;

Group Theory: Mathematical Expression of Symmetry in Physics

The present article reviews the multiple applications of group theory to the symmetry problems in physics. In classical physics, this concerns primarily relativity: Euclidean, Galilean, and Einsteinian (special). Going over to quantum mechanics, we first note that the basic principles imply that the state space of a quantum system has an intrinsic structure of pre-Hilbert space that one completes into a genuine Hilbert space. In this framework, the description of the invariance under a group G is based on a unitary representation of G. Next, we survey the various domains of application: atomic and molecular physics, quantum optics, signal and image processing, wavelets, internal symmetries, and approximate symmetries. Next, we discuss the extension to gauge theories, in particular, to the Standard Model of fundamental interactions. We conclude with some remarks about recent developments, including the application to braid groups.

Hydration and microstructural development of calcined clay cement paste in the presence of calcium-silicate-hydrate (C–S–H) seed

The microstructure of Portland and calcined clay cement paste incorporating calcium-silicate-hydrate (C–S–H) seed was investigated to understand the role of nucleation seed in cement hydration, and to study the potential synergy between C–S–H seed and calcined clay. The development of compressive strength of samples with and without seed was monitored until 28 days of hydration. Microstructural analysis techniques including thermogravimetric analysis (TGA), scanning electron microscopy-energy dispersive X-ray spectroscopy (SEM-EDS), and quantitative X-ray diffraction (QXRD) were used to study the phase assemblage and composition of the cement paste specimens. Image analysis (IA) of backscattered electron (BSE) micrographs was used to determine the hydration degree of cement at the age of 1 day and 28 days. The results showed that the introduction of C–S–H seed clearly accelerated the hydration of cement and enhanced the hydration degree of cement even at the later age. The presence of seed also modified the composition of the inner products (IP) formed around the anhydrous cement grains. The combination of calcined clay and C–S–H seed enabled high replacement levels (up to 40 wt%) of cement without compromising its mechanical properties.

DIGITAL PLATFORM DELIVERY GUYS: EXTENDED PRODUCTION POINT IN THE CITY

This visual essay uses accompaniment methodology to address the urban experience of a digital platform delivery guy in Valdivia, in the south of Chile. Through images, we question the notion of of production, which is fundamental for Labor Process Theory (LPT) studies. In this sense, this perspective has identified the place of production as a physical, unitary, and stable space for both traditional industries and services economies. Our urban journey, accompanying a digital platform delivery guy, observes the place of production as the attempt to suppress the physical space between the customer and the desired product, which can only be done by activating a vast urban experience by those who transport the products.