Preservers of partial orders on the set of all variance-covariance matrices

Let H+n(R) be the cone of all positive semidefinite n x n real matrices. Two of the best known partial orders that were mostly studied on subsets of square complex matrices are the L?wner and the minus partial orders. Motivated by applications in statistics we study these partial orders on H+ n (R). We describe the form of all surjective maps on H+ n (R), n > 1, that preserve the L?wner partial order in both directions. We present an equivalent definition of the minus partial order on H+ n (R) and also characterize all surjective, additive maps on H+ n (R), n ? 3, that preserve the minus partial order in both directions.

Preservers of partial orders on the set of all variance-covariance matrices

Let H+n(R) be the cone of all positive semidefinite n x n real matrices. Two of the best known partial orders that were mostly studied on subsets of square complex matrices are the L?wner and the minus partial orders. Motivated by applications in statistics we study these partial orders on H+n(R). We describe the form of all surjective maps on H+ n (R), n > 1, that preserve the L?wner partial order in both directions. We present an equivalent definition of the minus partial order on H+n(R) and also characterize all surjective, additive maps on H+ n (R), n ? 3, that preserve the minus partial order in both directions.

PENGARUH USIA TERHADAP HUBUNGAN MEKANISME KOPING DENGAN KECEMASAN KETIKA MENJALANI TERAPI HEMODIALISA BAGI PARA PENDERITA GAGAL GINJAL KRONIK DI KABUPATEN KUNINGAN JAWABARAT

Para penderita Gagal Ginjal Kronis (GGK) yang menjalani terapi hemodialisa secara rutin, rata-rata sudah memahahami bahwa penyakit yang dideritanya bersifat ireversibel (ginjalnya tidak akan berfungsi seperti seperti dulu lagi), dan hal tersebut akan menimbulkan kecemasan pada pasien. Berdasarkan hal tersebut maka diperlukan analisis untuk mengetahu faktor apa saja yang dapat mempengaruhi kecemasan pasien penderika GGK yang menjalani terapi hemodialisa. Penelitian ini menggunakan metode deskriptif analitik dengan pendekatan crossectional, alat statistic yang digunakan dalam penelitan ini adalah Chi-Square Complex. Sampel didalam penelitian ini adalah seluruh pasien gagal ginjal kronik yang menjalani terapi hemodialisa di rumah sakit yang berada di Kabupaten Kuningan Jawabarat yang berjumlah 89 pasien. Variabel terikat dalam penelitian ini adalah mekanisme koping, dan usia sebagai variabel confounding. Berdasarkan hasil penelitian ada hubungan antara mekanisme koping dengan tingkat kecemasan pasien penderita Gagal Ginjal Kronis (GGK) yang menjalani terapi hemodialisa (0,000). Ada hubungan antara mekanisme koping dengan tingkat kecemasan pasien pada usia kategori dewasa akhir (0,005), dan juga ada hubungan antara mekanisme koping dengan tingkat kecemasan pasien pada usia kategori dewasa akhir (0,002). Menurut pendapat peneliti variabel usia berhubungan dengan lamanya pasien berobat (menjalani terapi), pasien yang sudah berobat dalam jangka waktu lama, lebih bisa mengatasi kecemasanya dibandingkan pasien yang baru menjalani pengobatan. Perawat perlu memperhatikan (menganalisis) dampak fisiologis akibat terapi hemodialisa, edukasi berkesinambungan terhadap pasien dan keluarga pasien dengan mengunakan berbagai media, perlunya penerapan berbagai macam tehnik relaksasi terutama dengan menggunakan pendekatan spiritual agar kecemasan pasien dapat berkurang.

Quantum chemical study of the mechanism of the palladium-catalysed C−H acetoxylation of benzene

In this work, the mechanism of the palladium-catalysed acetoxylation of benzene C-H has been studied theoretically in detail. Based on experimental studies, a four-step mechanism for this reaction had been proposed, that is, C−H activation of benzene is the rate-determining step which forms an intermediate ( k1 pathway) which is subsequently oxidized to produce a high-valent Pd intermediate ( k2 pathway). Using quantum chemical calculations, all pathways were investigated, and the activation energy, activation enthalpy and activation Gibbs free energy for all steps were calculated and compared with each other. It was determined that the RDS proceeds through a square complex instead of a T-shaped complex. The activation energy related to the k2 pathway is higher than that of the RDS, and therefore, a new mechanism is proposed.

Weak group inverse

In this paper, we introduce the weak group inverse (called as the WG inverse in the present paper) for square complex matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a pre-order and the other is a partial order, and derive several characterizations of the two orders. The paper ends with a characterization of the core EP order using WG inverses.

Quaternionic arithmetic lattices of rank 2 and a fake quadric in characteristic 2

We construct a torsion-free arithmetic lattice in [Formula: see text] arising from a quaternion algebra over [Formula: see text]. It is the fundamental group of a square complex with universal covering [Formula: see text], a product of trees with constant valency [Formula: see text], which has minimal Euler characteristic. Furthermore, our lattice gives rise to a fake quadric over [Formula: see text] by means of non-archimedean uniformization.

Regularizing algorithm for mixed matrix pencils

P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker’s canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren’s algorithm to square complex matrices with respect to consimilarity transformations $\begin{array}{} \displaystyle A \mapsto SA{\bar S^{ - 1}} \end{array}$ and to pairs of m × n complex matrices with respect to transformations $\begin{array}{} \displaystyle (A,B) \mapsto (SAR,SB\bar R) \end{array}$, in which S and R are nonsingular matrices.

Simply transitive quaternionic lattices of rank 2 overq(t) and a non-classical fake quadric

By means of a quaternion algebra over$\mathbb{F}$q(t), we construct an infinite series of torsion free, simply transitive, irreducible lattices in PGL2($\mathbb{F}$q((t))) × PGL2($\mathbb{F}$q((t))). The lattices depend on an odd prime powerq=prand a parameter τ ∈$\mathbb{F}$q×, τ ≠ 1, and are the fundamental group of a square complex with just one vertex and universal coveringTq+1×Tq+1, a product of trees with constant valencyq+ 1.Our lattices give rise via non-archimedian uniformization to smooth projective surfaces of general type over$\mathbb{F}$q((t)) with ample canonical class, Chern numbers c12= 2 c2, trivial Albanese variety and non-reduced Picard scheme. Forq= 3, the Zariski–Euler characteristic attains its minimal value χ = 1: the surface is a non-classical fake quadric.