Cullis-Radić determinant of a rectangular matrix which has a number of identical columns

In this paper we present how identical columns affect the Cullis-Radić determinant of an $m\times n$ matrix, where $m\leq n$

Properties of the determinant of a rectangular matrix

In this paper we present new identities for the Radić’s determinant of a rectangular matrix. The results include representations of the determinant of a rectangular matrix as a sum of determinants of square matrices and description how the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column

Microbial Extremophiles in Evolutionary Aspect

The microflora of the cryosphere of planet Earth provides the best analogs for life forms that might be found in the permafrost or polar ice caps of Mars, near the surface of the cometary nuclei, or in the liquid water beneath the ice crusts of icy moons of Jupiter and Saturn. For astrobiology the focus on the study alkaliphilic microorganisms was enhanced by the findings of abundant carbonates and carbonate globules rimmed with possibly biogenic magnetites in association with the putative microfossils in the ALH84001 meteorite. Although the ALH84001 "nanofossils" were to small and simple to be unambiguously recognized as biogenic, they stimulated Astrobiology research and studies of microbial extremophiles and biomarkers in ancient rocks and meteorites. Recent studies of CI and CM carbonaceous meteorites have resulted in the detection of the well-preserved mineralized remains of coccoidal and" filamentous microorganisms in cyanobacterial mats. Energy Dispersive X-ray Analysis has shown anomalous biogenic element ratios clearly indicating they are not recent biological contaminants. This paper reviews microbial extremophiles in context of their significance to Astrobiology and the evolution of life. Extremophilic microorganisms on Earth are models for life that might endure high radiation environments in the ice near the surface of comets or on the icy moons of Jupiter and Saturn and in the seafloor deep beneath the icy crusts of Europa and Enceladus

Psychrophilic Biomass Producers in the Trophic Chain of the Microbial Community of Lake Untersee, Antarctica

The study of photosynthetic microorganisms from the Lake Untersee samples showed dispersed distribution of phototrophs within ~80 m water column. Lake Untersee represents a unique ecosystem that experienced complete isolation: sealed by the Anuchin Glacier for many millennia. Consequently, its biocenosis has evolved over a significant period of time without exchange or external interaction with species from other environments. The major producers of organic matter in Lake Untersee are represented by phototrophic and chemolithotrophic microorganisms. This is the traditional trophic scheme for lacustrine ecosystems on Earth. Among the phototrophs, diatoms were not found, which differentiates this lake from other known ecosystems. The dominant species among phototrophs was Chlamydomonas sp. with typical morphostructure: green chloroplasts, bright red round spot, and two polar flagella near the opening. As expected, the physiology of studied phototrophs was limited by low temperature, which defined them as obligate psychrophilic microorganisms. By the quantity estimation of methanogenesis in this lake, the litho-autotrophic production of organic matter is competitive with phototrophic production. However, pure cultures of methanogens have not yet been obtained. We discuss the primary producers of organic matter and the participation of our novel psychrophilic homoacetogen into the litho-autotrophic link of biomass production in Lake Untersee

Psychrophilic and Psychrotolerant Microbial Extremophiles in Polar Environments

The microbial extremophiles that inhabit the polar regions of our planet are of tremendous significance. The psychrophilic and psychrotolerant microorganisms, which inhabit all of the cold environments on Earth have important applications to Bioremediation, Medicine, Pharmaceuticals, and many other areas of Biotechnology. Until recently, most of the research on polar microorganisms was confined to studies of polar diatoms, yeast, fungi and cyanobacteria. However, within the past three decades, extensive studies have been conducted to understand the bacteria and archaea that inhabit the Arctic and Antarctic sea-ice, glaciers, ice sheets, permafrost and the cryptoendolithic, cryoconite and ice-bubble environments. These investigations have resulted in the discovery of many new genera and species of anaerobic and aerobic microbial extremophiles. Exotic enzymes, cold-shock proteins and pigments produced by some of the extremophiles from polar environments have the potential to be of great benefit to Mankind. Knowledge about microbial life in the polar regions is crucial to understanding the limitations and biodiversity of life on Earth and may provide valuable clues to the Origin of Life on Earth. The discovery of viable microorganisms in ancient ice from the Fox Tunnel, Alaska and the deep Vostok Ice has shown that microorganisms can remain alive while cryopreserved in ancient ice. The psychrophilic lithoautotrophic homoacetogen isolated from the deep anoxic trough of Lake Untersee is an ideal candidate for life that might inhabit comets or the polar caps of Mars. The spontaneous release of gas from within the Anuchin Glacier above Lake Untersee may provide clues to the ice geysers that erupt from the tiger stripe regions of Saturn s moon Enceladus. The methane productivity in the lower regimes of Lake Untersee may also provide insights into possible mechanisms for the recently discovered methane releases on Mars. Since most of the other water bearing bodies of our Solar system are frozen worlds, microbial extremophiles from the Polar Regions of Earth are of great importance to Astrobiology in understanding where and how to search for evidence of life elsewhere in the Cosmos

Exact values of girth for some graphs D(k,q) and upper bounds of the order of cages

Let q be a prime power and k∈{5,7,9,11}. In this paper it is shown that the girth of a graph D(k,q) is equal to k+5. As a consequence, explicit examples of graphs which provide the best known upper bounds of the order of (r,g)-cages, r≥5, g∈{10,14,16}, are given

Local solutions to Darboux problem with a discontinuous right-hand side

The existence of a local solution to the Darboux problem uxy (x, y) = g (u (x, y)), u (x, 0) = u (0, y) = 0, where g is Lebesgue measurable and has at most polynomial growth, is proved.Доведено iснування локального розв’язку проблеми Дарбу uxy (x, y) = g (u (x, y)), u (x, 0) = u (0, y) = 0, де g є вимiрна за Лебегом функцiя, що росте не швидше, нiж полiном

Anaerobic Cultures from Preserved Tissues of Baby Mammoth

Microbiological analysis of several cold-preserved tissue samples from the Siberian baby mammoth known as Lyuba revealed a number of culturable bacterial strains that were grown on anaerobic media at 4 C. Lactic acid produced by LAB (lactic acid bacteria) group, usually by members of the genera Carnobacterium and Lactosphera, appears to be a wonderful preservative that prevents other bacteria from over-dominating a system. Permafrost and lactic acid preserved the body of this one-month old baby mammoth and kept it in exceptionally good condition, resulting in this mammoth being the most complete such specimen ever recovered. The diversity of novel anaerobic isolates was expressed on morphological, physiological and phylogenetic levels. Here we discuss the specifics of the isolation of new strains, differentiation from trivial contamination, and preliminary results for the characterization of cultures

Psychrotolerant Anaerobes from Lake Podprudnoe, Antarctica and Penguin Spheniscus demersus Colony, South Africa

The study of a sample collected from a wind-made ice sculpture near Lake Podprudnoe, Antarctica led to the isolation of the psychrotolerant strain ISLP-3. Cells of the new isolate are vibrio-shaped that measure 0.5 x 1.0-3.0 micron in size. Growth occurs within the temperature range 5-35 C with the optimum at 22 C. Salinity range for growth is 0-2 % NaCl with the optimum at 0.25 %. The new isolate grows within a pH range from 6.0 to 9.5 with the optimum at 7.5. Strain ISLP-3 is saccharolytic, growing on the following substrates: D-glucose, D-ribose, D-fructose, D-arabinose, maltose, sucrose, D-trehalose, D-mannose, D-cellobiose, lactose, starch, chitin, triethylamine, N-acetylglucosamine, and urea. The best growth occurred on D-cellobiose. An environmental sample of pond water near a colony of the endemic species of African penguins, Spheniscus demersus, was collected in February 2008 and delivered directly to the Astrobiology laboratory at NSSTC. The microbiological study of this sample led to the isolation of two psychrotolerant strains ARHSd-7G and ARHSd-9G. Both strains are strictly anaerobic bacteria and are able to grow at high pH and low temperatures. The cells of strain ARHSd-7G are motile, vibrio-shaped, spore-forming cells. Optimal growth of this strain occurs at 30 C, 3 % NaCl, and pH 8.9. The isolate ARHSd-7G combines sugarlytic and proteolytic metabolisms, growing on some proteolysis products including peptone and yeast extract and a number of sugars. The second isolate, ARHSd-9G, exhibits thin, elongated rods that measure 0.4 x 3-5 micron. The cells are motile and spore-forming. Optimal growth of strain ARHSd-9G occurs at 30 C, 1.75 % NaCl, and pH 8.5. The strain ARHSd-9G is sugarlytic, growing well on substrates such as D-glucose, sucrose, D-cellobiose, maltose, fructose, D-mannose, and trehalose (the only exception is positive growth on yeast extract). In this report, the physiological and morphological characteristics of the novel psychrotolerant, alkaliphilic, and neutrophilic isolates from the Antarctica 2008 expedition will be discussed

Microbial Extremophiles in Aspect of Limits of Life

During Earth's evolution accompanied by geophysical and climatic changes a number of ecosystems have been formed. These ecosystems differ by the broad variety of physicochemical and biological factors composing our environment. Traditionally, pH and salinity are considered as geochemical extremes, as opposed to the temperature, pressure and radiation that are referred to as physical extremes (Van den Burg, 2003). Life inhabits all possible places on Earth interacting with the environment and within itself (cross species relations). In nature it is very rare when an ecotope is inhabited by a single species. As a rule, most ecosystems contain the functionally related and evolutionarily adjusted communities (consortia and populations). In contrast to the multicellular structure of eukaryotes (tissues, organs, systems of organs, whole organism), the highest organized form of prokaryotic life in nature is the benthic colonization in biofilms and microbial mats. In these complex structures all microbial cells of different species are distributed in space and time according to their functions and to physicochemical gradients that allow more effective system support, self-protection, and energy distribution. In vitro, of course, the most primitive organized structure for bacterial and archaeal cultures is the colony, the size, shape, color, consistency, and other characteristics of which could carry varies specifics on species or subspecies levels. In table 1 all known types of microbial communities are shown (Pikuta et a]., 2005). In deep underground (lithospheric) and deep-sea ecosystems an additional factor - pressure, and irradiation - could also be included in the list of microbial communities. Currently the beststudied ecosystems are: human body (due to the medical importance), and fresh water and marine ecosystems (due to the reason of an environmental safety). For a long time, extremophiles were terra incognita, since the environments with aggressive parameters (compared to the human body temperature, pH, mineralization, and pressure) were considered a priori as a dead zone