Quasi-split symmetric pairs of 𝑈(𝔰𝔩_{𝔫}) and Steinberg varieties of classical type

We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type A n − 1 A_{n-1} . This is obtained inside the limit of a projective system of Borel-Moore homologies of the Steinberg varieties of n n -step isotropic flag varieties. Arising from the construction are a basis of homological origin for the idempotent form and a geometric realization of rational modules.

On Fermat-Torricelli Problem in Frechet Spaces

We study the Fermat-Torricelli problem (FTP) for Frechet space X, where X is considered as an inverse limit of projective system of Banach spaces. The FTP is defined by using fixed countable collection of continuous seminorms that defines the topology of X as gauges. For a finite set A in X consisting of n distinct and fixed points, the set of minimizers for the sum of distances from the points in A to a variable point is considered. In particular, for the case of collinear points in X, we prove the existence of the set of minimizers for FTP in X and for the case of non collinear points, existence and uniqueness of the set of minimizers are shown for reflexive space X as a result of strict convexity of the space.

STRUKTUR DAN FUNGSI MANTRA HIDU-MAHIDU TATAMBA ANAK PADA MASYARAKAT DAYAK BAKUMPAI

Penelitian ini bertujuan mendeskripsikan struktur dan fungsi mantra hidu-mahidu tatamba anak pada masyarakat Dayak Bakumpai. Metode yang digunakan dalam penelitian ini adalah deskriptif kualitatif dengan pendekatan struktural semiotik. Sumber data yang digunakan dalam penelitian ini adalah sumber data primer dan sekunder. Data penelitian ini adalah tuturan-tuturan dalam mantra hidu-mahidu tatamba anak masyarakat Dayak Bakumpai yang berupa kata, frasa, kalimat, dan ungkapan dalam mantra tersebut. Metode pengumpulan data dalam penelitian ini, yaitu teknik observasi, teknik wawancara tidak terarah, dan teknik studi pustaka. Dari hasil analisis, ditemukan bahwa struktur mantra hidu-mahidu tatamba anak terdiri atas diksi dan imajinasi. Diksi yang terdapat dalam mantra hidu-mahidu tatamba anak meliputi kata umum dan kata khusus. Imajinasi yang terdapat dalam mantra hidu-mahidu tatamba anak meliputi (1) imajinasi visual, (2) imajinasi auditif, dan (3) imajinasi taktil. Fungsi yang terdapat dalam mantra hidu-mahidu tatamba anak meliputi (1) fungsi sebagai sistem proyeksi (projective system); (2) sebagai alat pengesahan pranata-pranata dan lembaga-lembaga kebudayaan; (3) sebagai alat pendidikan anak (pedagogical device); dan (4) sebagai alat pemaksa dan pengawas agar norma-norma masyarakat akan selalu dipatuhi anggota kolektifnya.This study aims to describe the structure and function of the mantra hidu-mahidu tatamba anak in Dayak Bakumpai community. The method used in this research is descriptive qualitative with a semiotic structural approach. Sources of data used in this study are primary and secondary data sources. The data of this research are the utterances in the mantra hidu-mahidu tatamba anak of the Dayak Bakumpai community, in the form of words, phrases, sentences, and expressions in the mantra. Data collection techniques in this study, namely observation techniques, unfocused interview techniques, and literature study techniques. From the analysis, it was found that the structure of the mantra hidu-mahidu tatamba anak consisted of diction and imagination. The diction contained in the mantra hidu-mahidu includes general words and special words. The imagination contained in the mantra hidu-mahidu tatamba anak includes (1) visual imagination, (2) auditive imagination, and (3) tactile imagination. Meanwhile, the functions contained in the mantra hidu-mahidu tatamba anak include (1) function as a projective system; (2) as a means of ratifying cultural institutions and institutions; (3) as a pedagogical device; and (4) as a means of coercion and supervision so that the norms of society will always be obeyed by their collective members.

Weights of the $\mathbb{F}_{q}$-forms of $2$-step splitting trivectors of rank $8$ over a finite field

Grassmann codes are linear codes associated with the Grassmann variety $G(\ell,m)$ of $\ell$-dimensional subspaces of an $m$ dimensional vector space $\mathbb{F}_{q}^{m}.$ They were studied by Nogin for general $q.$ These codes are conveniently described using the correspondence between non-degenerate $[n,k]_{q}$ linear codes on one hand and non-degenerate $[n,k]$ projective systems on the other hand. A non-degenerate $[n,k]$ projective system is simply a collection of $n$ points in projective space $\mathbb{P}^{k-1}$ satisfying the condition that no hyperplane of $\mathbb{P}^{k-1}$ contains all the $n$ points under consideration. In this paper we will determine the weight of linear codes $C(3,8)$ associated with Grassmann varieties $G(3,8)$ over an arbitrary finite field $\mathbb{F}_{q}$. We use a formula for the weight of a codeword of $C(3,8)$, in terms of the cardinalities certain varieties associated with alternating trilinear forms on $\mathbb{F}_{q}^{8}.$ For $m=6$ and $7,$ the weight spectrum of $C(3,m)$ associated with $G(3,m),$ have been fully determined by Kaipa K.V, Pillai H.K and Nogin Y. A classification of trivectors depends essentially on the dimension $n$ of the base space. For $n\leq 8 $ there exist only finitely many trivector classes under the action of the general linear group $GL(n).$ The methods of Galois cohomology can be used to determine the classes of nondegenerate trivectors which split into multiple classes when going from $\mathbb{\bar{F}}$ to $\mathbb{F}.$ This program is partially determined by Noui L. and Midoune N. and the classification of trilinear alternating forms on a vector space of dimension $8$ over a finite field $\mathbb{F}_{q}$ of characteristic other than $2$ and $3$ was solved by Noui L. and Midoune N. We describe the $\mathbb{F}_{q}$-forms of $2$-step splitting trivectors of rank $8$, where char $\mathbb{F}_{q}\neq 3.$ This fact we use to determine the weight of the $\mathbb{F}_{q}$-forms.

LANGGAM CERITA RAKYAT BANYUMAS DALAM HARMONI NILAI KEARIFAN LOKAL

Artikel ini bertujuan untuk mendeskripsikan fungsi cerita rakyat bagi masyarakat di Kabupaten Banyumas. Artikel ini merupakan kualitatif deskriptif. Dalam artikel ini informasi dideskripsikan secara teliti dan analisis. Data Makalah dikumpulkan melalui beberapa sumber yaitu, informan, tempat benda-benda fisik, dan dokumen. Teknik pengumpulan data yang digunakan meliputi observasi langsung, perekaman, wawancara dan analisis dokumen. Teknik cuplikan (sampling) yang digunakan adalah purposive sampling. Teknik validasi data yang digunakan adalah triangulasi data/sumber dan triangulasi metode. Teknik validasi data yang digunakan adalah review informan. Teknik analisis yang digunakan adalah analisis model interaktif (interactive model of analysis). Cerita rakyat Kabupaten Banyumas yang dihimpun dan dianalisis dalam Makalah ini berjumlah tiga, yaitu (1) cerita rakyat “Babad Ajibarang: Djaka Mruyung”, (2) cerita rakyat “Babad Sokaraja: Raden Kuncung”, dan(3) cerita rakyat “Batu Raden”. Pengkajian cerita rakyat yang di dalamnya termuat cerita rakyat (folk literature) memiliki fungsi antara lain: (1) sebagai sistem proyeksi (projective system), (2) sebagai alat pengesahan pranata- pranata dan lembaga-lembaga kebudayaan, (3) sebagai alat pendidik anak (pedagogical device) (4) sebagai alat pemeriksa dan pengawas agar norma-norma masyarakat akan selalu dipatuhi anggota kolektifnya. Keempat fungsi inilah yang ditemukan dalam kajian ini.

The Relief-Perspectives of Bitonti and Borromini

The research represents principles of projective-geometric design of illusory spaces and proposes a study about the relief-perspective which featured the applications of science and art to interior decoration and architectural spaces during the sixteenth and the seventeenth century. The research has analyzed a selection of figurative and built illusory spaces, going to deepen the formation of the concepts of perception and illusion. During Renaissance was given emphasis to projective methods, of which were investigated the principles of geometric and optical ones in the proportions and in the visualization of architectural works, and the use of projective system accelerating or slowing the effects of the natural perspective to modify certain environmental aspects, external and internal, to the built volumes. The research also compares two major applications, the relief-perspectives of Francesco Borromini and Giovanni Maria da Bitonto and their partnership in the design of the perspectival tabernacle in Bologna and in the perspectival gallery for the Spada palace in Rome.

Darboux chart on projective limit of weak symplectic Banach manifold

Suppose M be the projective limit of weak symplectic Banach manifolds {(Mi, ϕij)}i, j∈ℕ, where Mi are modeled over reflexive Banach space and σ is compatible with the projective system (defined in the article). We associate to each point x ∈ M, a Fréchet space Hx. We prove that if Hx are locally identical, then with certain smoothness and boundedness condition, there exists a Darboux chart for the weak symplectic structure.