Virginia Research Institute

The longstanding nonnegative inverse eigenvalue problem (NIEP) is to determine which multisets of complex numbers occur as the spectrum of an entry-wise nonnegative matrix. Although there are some well-known necessary conditions, a solution to the NIEP is far from known. An invertible matrix is called a Perron similarity if it diagonalizes an irreducible, nonnegative matrix. Johnson and Paparella [Linear Algebra Appl. 493 (2016), pp. 281–300] developed the theory of real Perron similarities. Here, we fully develop the theory of complex Perron similarities. Each Perron similarity gives a nontrivial polyhedral cone and convex polytope of realizable spectra (thought of as vectors in complex Euclidean space). The extremals of these convex sets are finite in number, and their determination for each Perron similarity would solve the diagonalizable NIEP, a major portion of the entire problem. By considering Perron similarities of certain realizing matrices of Type I Karpelevič arcs, large portions of realizable spectra are generated for a given positive integer. This is demonstrated by producing a nearly complete geometrical representation of the spectra of four-by-four stochastic matrices. Similar to the Karpelevič region, it is shown that the subset of complex Euclidean space comprising the spectra of stochastic matrices is compact and star-shaped. Extremal elements of the set are defined and shown to be on the boundary. It is shown that the polyhedral cone and convex polytope of the discrete Fourier transform (DFT) matrix corresponds to the conical hull and convex hull of its rows, respectively. Similar results are established for multifold Kronecker products of DFT matrices and multifold Kronecker products of DFT matrices and Walsh matrices. These polytopes are of great significance with respect to the NIEP because they are extremal in the region comprising the spectra of stochastic matrices. Implications for further inquiry are also given.

This chapter presents a discussion of a new model titled, “DETECT (Determining and Evaluating Truthfulness through Explicit Cue Testing) which relies upon the assessment of verbal and non-verbal cues. The author presents the argument that the digital age has posed novel challenges to law enforcement and intelligence personnel; hence, the author further explains the ways in which the DETECT model (©, Eugenie de Silva, 2014) can be used to determine deceptive activities at the individual-level even in a technologically advanced society. The chapter touches upon Denial and Deception (D&D), and how the detection of deception must be carried out in the twenty-first century, especially through rigorous monitoring within the established legal framework.

The article presents the sermon of the Dominican preacher Gabriel Zawieszko (Leopolita). The sermon is first from the cycle of ten, concerning St. Mary Magdalene. The preacher uses the concept and the metaphor of a mirror. A mirror is a symbol (at the same time) of a sinful (a mirror of the lust of the flesh, a mirror of the lust of the eyes and a mirror of the pride of life), a penance (nosce te ipsum) and a perfection (Christ — speculum sine macula). Zawieszko also invokes Greek maxim gnothi seauton (Know Thyself). It becomes the guiding thought of the sermon. He connects it with emblematic presentation of mirror (Lascivia, Superbia, Prudentia, Scientia).

Autorka analizuje tekst książki Jana Pawła II Pamięć i tożsamość pod kątem problemu patriotyzmu jako wartości ważnej w procesie wychowania. Interesuje ją nie tylko definicja patriotyzmu, ale także sposób jej formułowania. Swoje rozważania dzieli na dwie części, z których pierwsza dotyczy metafizyczno-teologicznego charakteru refleksji papieskiej na temat patriotyzmu, a druga poświęcona jest kwestii nadprzyrodzonego wymiaru patriotyzmu. Ostatecznie autorka podkreśla, że papież postrzega patriotyzm jako wartość moralną, którą można rozpatrywać także w perspektywie religijnej. W oparciu o tekst Pamięci i tożsamości autorka próbuje sprecyzować kwestie istotne w odczytywaniu religijnego kontekstu cnoty patriotyzmu. Jej zdaniem są to: cel ludzkiego życia, obecność zła, relacje jednostki do społeczności.

This chapter presents a discussion of the START model, which has been internationally recognized as a useful syllabi-tracking system that can be applied to online and on-ground teaching. START, an acronym for “(S)yllabus Analysis (T)racking System Covering Objectives (A)ssessment Methods (R)esearch Component Inclusion, (T)esting Through Research,” is presented in this chapter as a unique method for educators to heighten current academic standards by placing a priority on multidisciplinary approaches. Through this chapter, the authors sought to provide readers with an understanding of the application of the START model in the twenty-first century. Additionally, to further strengthen the presented information, the authors included reflections on past experiences in the application of the model at a university level.

W artykule zaprezentowano analizy uzyskanych wyników badań przeprowadzonych wśród marginalizowanych Romów słowackich przy użyciu systemu wartości ludzkich Shaloma H. Schwartza (1992). Rezultaty tych badań mogą być przydatne w wielu aspektach życia publicznego, w formułowaniu metodologii systemu szkolnego i w formułowaniu wytycznych dotyczących Romów, w opiece zdrowotnej i usługach medycznych, we wzmacnianiu prewencji problemów dla szczególnych terenów segregowanych. Rozpatrując różne typy społeczności romskich, wyniki badań w obrębie systemu wartości Romów i jego potencjalne zróżnicowanie mogą stanowić empirycznie weryfikowalne kryterium homogeniczności etnicznej i kulturowej badanej etniczności na Słowacji. Mogą one także przyczynić się do rozwiania stereotypów i uprzedzeń większości wobec ludności romskiej.

A scanning electron microscope study of oxide replicas of aluminum electrolytic capacitor foils has provided information on tunneling produced by a given etch. Tunnel morphology depends on microstructure of the aluminum and on etching conditions. With increasing current density in an electrochemical etch, the number of etching tunnels per unit area increases and tunnel diameter decreases. A simplified model predicts the number of tunnels per unit area and the tunnel diameter needed for maximum capacitance for a given anodic film thickness.