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Search results for: LIPSCHITZ POLYHEDRA
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POLYHEDRON
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On weak solutions of the boundary value problem within linear dilatational strain gradient elasticity for polyhedral Lipschitz domains
PublicationWe provide the proof of an existence and uniqueness theorem for weak solutions of the equilibrium problem in linear dilatational strain gradient elasticity for bodies occupying, in the reference configuration, Lipschitz domains with edges. The considered elastic model belongs to the class of so-called incomplete strain gradient continua whose potential energy density depends quadratically on linear strains and on the gradient of...
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Polyhedral Ramsey Numbers
PublicationGiven two polygons or polyhedrons P1 and P2, we can transform these figures to graphs G1 and G2, respectively. The polyhedral Ramsey number Rp(G1,G2) is the smallest integer n such that every graph, which represents polyhedron on n vertices either contains a copy of G1 or its complement contains a copy of G2. Using a computer search together with some theoretical results we have established some polyhedral Ramsey numbers, for example...
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CuO-decorated MOF derived ZnO polyhedral nanostructures for exceptional H2S gas detection
PublicationConsidering that H2S is a hazardous gas that poses a significant risk to people's lives, research into H2S gas sensors has garnered a lot of interest. This work reports a CuO/ZnO multifaceted nanostructures(NS) created by heat treating Cu2+/ZIF-8 impregnation precursors, and their microstructure and gas sensing characteristics were examined using various characterization techniques (XRD, XPS, SEM, TEM, and BET). The as-prepared...
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Equivalence of equicontinuity concepts for Markov operators derived from a Schur-like property for spaces of measures
PublicationVarious equicontinuity properties for families of Markov operators have been – and still are – used in the study of existence and uniqueness of invariant probability for these operators, and of asymptotic stability. We prove a general result on equivalence of equicontinuity concepts. It allows comparing results in the literature and switching from one view on equicontinuity to another, which is technically convenient in proofs....
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Limits Theorems for Random Walks on Homeo(S1)
PublicationThe central limit theorem and law of the iterated logarithm for Markov chains corresponding to random walks on the space Homeo(S1) of circle homeomorphisms for centered Lipschitz functions and every starting point are proved.
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Application of the numerical-analytic method for systems of differential equations with parameter
PublicationThe numerical-analytic method is applied to systems of differential equations with parameter under the assumption that the corresponding functions satisfy the Lipschitz conditions in matrix notation. We also obtain several existence results for problems with deviations of an argument
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Constructive Controllability for Incompressible Vector Fields
PublicationWe give a constructive proof of a global controllability result for an autonomous system of ODEs guided by bounded locally Lipschitz and divergence free (i.e. incompressible) vector field, when the phase space is the whole Euclidean space and the vector field satisfies so-called vanishing mean drift condition. For the case when the ODE is defined over some smooth compact connected Riemannian manifold, we significantly strengthen...
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Existence of unbounded solutions to parabolic equations with functional dependence
PublicationThe Cauchy problem for nonlinear parabolic differential-functional equations is considered. Under natural generalized Lipschitz-type conditions with weights, the existence and uniqueness of unbounded solutions is obtained in three main cases: (i) the functional dependence u(·); (ii) the functional dependence u(·) and ∂xu(·); (iii) the functional dependence u(·)and the pointwise dependence ∂xu(t,x).
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Generalized Gradient Equivariant Multivalued Maps, Approximation and Degree
PublicationConsider the Euclidean space Rn with the orthogonal action of a compact Lie group G. We prove that a locally Lipschitz G-invariant mapping f from Rn to R can be uniformly approximated by G-invariant smooth mappings g in such a way that the gradient of g is a graph approximation of Clarke’s generalized gradient of f . This result enables a proper development of equivariant gradient degree theory for a class of set-valued gradient...
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Lead(II) coordination polymers with imidazole-4- and pyrazole-3-carboxylate isomeric linkers: Structural diversity and luminescence properties
PublicationUsing 1H-imidazole-4-carboxylic acid (4imCOOH) and 1H-pyrazole-3-carboxylic acid (3pyrCOOH) coordination polymers [Pb(4imCOO)2(H2O)]n (1) and [Pb2(3pyrCOO)4]n (2) were constructed. Obtained polymers were characterized via FT-IR, X-ray, PL and TG methods. The coordination polyhedron around Pb(II) in 1 is described as distorted pentagonal pyramid with hemidirected coordination sphere (based on DFT calculations). Compound 2 consists...
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Comparision principles for parabolic differential - functional initial - value problems.
PublicationBadamy paraboliczne równania z zależnością funkcyjną i podajemy kryteria jednoznaczności przy warunkach porównawczych typu Perrona i Lipschitza dla nieliniowej prawej strony. W przypadku gdy zależność funkcyjna dotyczy również pochodnej funkcji niewiadomej, to stosujemy nierówności typu Henry'ego.
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Existence of solutions of differential equations with nonlinearmultipoint boundary conditions.
PublicationSformułowano warunki dostateczne na istnienie rozwiązań (jedynego lubekstremalnych) dla równań różniczkowych z warunkami jak wyżej przyzastosowaniu metody iteracji monotonicznych. O prawej stronie zagadnienia i nieliniowym warunku brzegowym zakładano między innymi, że spełniają jednostronny warunek Lipschitza.
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Differential inequalities with initial time difference.
PublicationUzyskano pewne wyniki porównawcze pomiędzy rozwiązaniami nierówności różniczkowych startujących z różnych punktów początkowych. O nieliniowej funkcji f (związanej z zagadnieniem) zakładano jednostronny warunek Lipschitza. Podano pewne zastosowanie otrzymanych wyników. Sformułowano też pewne warunki dotyczące stabilności.
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A quaternion-based modified feistel cipher for multimedia transmission
PublicationIn this paper a quaternion-based modified Feistel Cipher is proposed. The algorithm is based on the scheme proposed by Sastry and Kumar (2012). Our algorithm uses special properties of quaternions to perform rotations of data sequences in 3D space for each of the cipher rounds. The plaintext (image in gray-tone) is divided into two square matrices of equal size which consist of Lipschitz quaternions. A modular arithmetic was implemented...
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Existence of solutions of differential equations with boundary conditions
PublicationPraca dotyczy równań różniczkowych z liniowym warunkiem brzegowym zależnym od parametru. Podane zostały warunki dostateczne na istnienie rozwiązania powyższego zagadnienia. Przy dowodzie i konstrukcji iteracji monotonicznych zastosowano metodę górnych i dolnych rozwiązań. O prawej stronie zagadnienia zakładano jednostronny warunek Lipschitza.
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Numerical-analytic methods for differential-algebraic systems
PublicationMetodę numeryczno-analityczną połączoną z metodą porównawczą zastosowano do układów równań różniczkowo-algebraicznych z linowymi warunkami brzegowymi otrzymując warunki dostateczne na istnienie rozwiązania. O prawych stronach zagadnienia zakładano warunek Lipschitza. Otrzymano oszacowania błędów. Problem z odchylonymi argumentami był również przedmiotem rozważań tej pracy.
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Differential equations with integral boundary conditions
PublicationStosuje się metodę iteracji monotonicznych opartą na dolnym i górnym rozwiązaniu. Przy jednostronnym warunku Lipschitza uzyskano pewne wyniki dotyczące rozwiązań zwyczajnych równań różniczkowych z całkowym warunkiem brzegowym. Sformułowano warunki dostateczne na istnienie jedynego rozwiązania (lub rozwiązań ekstremalnych) w pewnym segmencie. Podano przykłady ilustrujące przyjęte założenia.
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Samoilenko`s method to differential algebraic systems with integral boundary conditions.
PublicationProblemy różniczkowo-algebraiczne z warunkami brzegowymi (typu całkowego) są przedmiotem badań. Zastosowano metodę Samoilenki w powiązaniu z metodą porównawczą. O prawych stronach zagadnienia zakładano, że spełniają warunek Lipschitza oraz promień spektralny odpowiedniej macierzy jest mniejszy od 1.Podane zostały warunki dostateczne na istnienie rozwiązania omawianego zagadnienia.
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Heat capacities and thermodynamic properties of antimony substituted lanthanum orthoniobates
PublicationThe results of heat capacity measurements for the lanthanum orthoniobate substituted with 10, 20 and 30 mol% of antimony (LaNb0.9Sb0.1O4, LaNb0.8Sb0.2O4 and LaNb0.7Sb0.3O4) are presented and discussed. Temperature dependence of low temperature heat capacity was analyzed within the Debye and Einstein models. The Debye temperature decreased, whereas the Einstein temperature increased with antimony content. The decrease of the Debye...
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Delay integro-differential inequalities with initial time difference and applications.
PublicationPraca dotyczy nierówności różniczko-całkowych z opóźnionymi argumentami przy różnych warunkach początkowych. Przy pewnych założeniach (m.in. monotoniczność, jednostronny warunek Lipschitza) sformułowano twierdzenia porównawcze dla rozwiązań w.w nierówności. Pokazano zastosowania w technice iteracji monotonicznych i sformułowano warunki dostateczne na istnienie rozwiązań ekstremalnych dla równań różniczkowo-całkowych z odchylonymi...
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Monotone method for second-order delayed differential equations with boundary value conditions.
PublicationIstnienie rozwiązań problemów brzegowych dla równań różniczkowych drugiego rzędu z opóźnionymi argumentami jest dyskutowane w tej pracy. Nierówności różniczkowe rzędu drugiego z odchylonymi argumentami są również przedmiotem badań. Uzyskane wyniki otrzymano stosując technikę iteracji monotonicznych przy założeniu, że prawa strona zagadnienia spełnia jednostronny warunek Lipschitza. Sformułowano też twierdzenia o istnieniu rozwiązań...
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Systems of differential equations with a singular matrix
PublicationPraca dotyczy układów równań różniczkowych z macierzą osobliwą. Szczególnymi przypadkami takich układów są równania różniczkowo-algebraiczne. Korzystając z odpowiedniej nierówności różniczkowej dla układów równań i metody quasi linearyzacji pokazano, iż odpowiednie monotoniczne ciągi są zbieżne do rozwiązania naszego problemu i jest to zbieżność kwadratowa. O funkcji f występującej po prawej stronie zagadnienia zakładano...
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Differential-algebraic systems with maxima
PublicationMetoda numeryczno-analityczna została zastosowana do układów równań różniczkowo-algebraicznych z operatorem maximum. Zakładając warunek Lipschitza na funkcje występujące w zagadnieniu pokazano, że ciąg iteracji prostych jest zbieżny do rozwiązania zagadnienia pomocniczego. Podano warunki dostateczne na istnienie rozwiązania problemu wyjściowego. Iteracje Seidla też były przedmiotem badań. W ostatniej części pracy był dyskutowany...
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Monotone and numerical analytic- methods for differential equations.
PublicationPraca dotyczy problemu różniczkowo-całkowego (typu Fredholma) z ogólnym warunkiem początkowo-brzegowo-całkowym. W pierwszej części pracy, stosując metodę iteracji monotonicznych, sformułowano warunki dostateczne które gwarantują, że dyskutowany problem ma rozwiązanie ekstremalne w zbiorze generowanym przez dolne i górne rozwiązania. Rozważania teoretyczne poparto przykładem i dyskusją. W drugiej części pracy zastosowano metodę...
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Computational issues of solving the 1D steady gradually varied flow equation
PublicationIn this paper a problem of multiple solutions of steady gradually varied flow equation in the form of the ordinary differential energy equation is discussed from the viewpoint of its numerical solution. Using the Lipschitz theorem dealing with the uniqueness of solution of an initial value problem for the ordinary differential equation it was shown that the steady gradually varied flow equation can have more than one solution....
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A robust sliding mode observer for non-linear uncertain biochemical systems
PublicationA problem of state estimation for a certain class of non-linear uncertain systems has been addressed in this paper. In particular, a sliding mode observer has been derived to produce robust and stable estimates of the state variables. The stability and robustness of the proposed sliding mode observer have been investigated under parametric and unstructured uncertainty in the system dynamics. In order to ensure an unambiguous non-linear...
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Squamous cell carcinoma, NOS - Female, 70 - Tissue image [6280729578143131]
Open Research DataThis is the histopathological image of SKIN tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Squamous cell carcinoma, NOS - Female, 70 - Tissue image [6280729578144471]
Open Research DataThis is the histopathological image of SKIN tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Squamous cell carcinoma, NOS - Female, 70 - Tissue image [6280729578141071]
Open Research DataThis is the histopathological image of SKIN tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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Squamous cell carcinoma, NOS - Female, 70 - Tissue image [6280729578148991]
Open Research DataThis is the histopathological image of SKIN tissue sample obtained in Medical University Gdańsk and deposited in ZMDL-GUMED. The sample image was taken using: Pannoramic 250 3DHistech slide scanner (20x magnification) and saved to DICOM format.
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A new quaternion-based encryption method for DICOM images
PublicationIn this paper, a new quaternion-based lossless encryption technique for digital image and communication on medicine (DICOM) images is proposed. We have scrutinized and slightly modified the concept of the DICOM network to point out the best location for the proposed encryption scheme, which significantly improves speed of DICOM images encryption in comparison with those originally embedded into DICOM advanced encryption standard...
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Proximal primal–dual best approximation algorithm with memory
PublicationWe propose a new modified primal–dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates computed in previous steps in the formulas defining current iterate. To this end we consider projections onto intersections of halfspaces generated on the basis of the current as well as the previous...
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Low-Dimensional Magnetic Semimetal Cr0.65Al1.35Se3
PublicationWhile exploring novel magnetic semiconductors, the new phase Cr0.65Al1.35Se3 was discovered and characterized by both structural and physical properties. Cr0.65Al1.35Se3 was found to crystallize into orthorhombic CrGeTe3-type structure with space group Pnma (no. 62). Vacancies and mixed occupancies were tested, and the results show that one of the 4c sites accommodates a mixture of Cr and Al atoms, while the other 4c site is fully...
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Copper(II) complexes with substituted imidazole and chlorido ligands: X-ray, UV-Vis, magnetic and EPR studies and chemotherapeutic potential
PublicationCrystal structures, UV-Vis and EPR spectra and magnetic properties of four copper(II) complexes with chloride anions and 4-methylimidazole, 2-ethylimidazole, 2-isopropylimidazole or 2-ethyl-4-methylimidazole are described. In the solid state three of the complexes are mononuclear and one complex with 2-ethylimidazole is binuclear with bridging chlorido ions. UV-Vis spectra of the methanolic solutions of the complexes show LMCT...
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Structural Insights into New Bi(III) Coordination Polymers with Pyridine-2,3-Dicarboxylic Acid: Photoluminescence Properties and Anti-Helicobacter pylori Activity
PublicationTwo novel coordination polymers, [Bi2(2,3pydc)2(2,3pydcH)2(H2O)]n(1) and {(Et3NH)2[Bi(2,3pydc)(2,3pydcH)Cl2]}n(2) were prepared using as a prolinker pyridine-2,3-dicarboxylic acid(2,3pydcH2). The obtained complexes were fully characterized by elemental analysis, TG/DTG, FT-IR,solid-state photoluminescence, DFT calculations and single-crystal X-ray diffraction. The obtainedcomplexes crystallized in the triclinicP-1 space group (1)...
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General route for the synthesis of terminal phosphanylphosphido complexes of Zr(IV) and Hf(IV): Structural investigations of the first zirconium complex with a phosphanylphosphido ligand
PublicationReactions of R2P-P(SiMe3)Li with [Cp2MCl2] (M = Zr, Hf) in hydrocarbons yield the related terminal phosphanylphosphidocomplexes [Cp2M(Cl){(Me3Si)P-PR2-jP1}] (R = iPr and tBu). The solid state structures of [Cp2M(Cl){P(SiMe3)-PiPr2-jP1}] (M = Zr, Hf) were established by single crystal X-ray diffraction studies. The phosphido-P atoms adopt almost planar geometries and the phosphanyl P atoms adopt pyramidal geometries. The reaction...
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Nickel(II) tri-tert-butoxysilanethiolates with N-heterocyclic bases as additional ligands: Synthesis, molecular structure and spectral studies
PublicationW publikacji przedstawiono metodę syntezy trzech kompleksów silanotiolanowych z takimi N-heterocyklicznymi zasadami jak: pirydyna, 2-metylopirydyna i 3,5-dimetylopirydyna. Dla tych kompleksów przeprowadzono badania X-Ray, analizy elementarnej. Przy pomocy rentgenowskiej analizy strukturalnej wykazano różną koordynację atomu centralnego - niklu.
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Synthesis, crystal structure and spectroscopic characterization of new anionic iridium(III) complexes and their interaction with biological targets
PublicationThe synthesis and characterisation of new anionic iridium(II) complexes (NH4)2[IrCl4(κ2N,N’-H2biim)]2 · 5H2O (1) and ((CH3)2NH2)[IrCl4(κ2N,N’-PyBIm)] · H2O (2) are presented in this article. Spectroscopic methods (1H, 13C and 15N NMR, FTIR, UV-Vis) were used to characterize these new complexes. Solid-state structural analysis (SC-XRD) of complexes 1 and 2 shows a slightly distorted octahedral geometry of Ir(III) ions, which is...
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Nitrate and nitrite silver complexes with weakly coordinating nitriles
PublicationSimple system of weak nitrile ligands and silver nitrite/nitrate allowed the formation and isolation of coordination compounds of diverse nuclearity and dimensionality. The extension of the network does not enhance the luminescent properties of the ligands however it gives rise to the new MLCT bands in the visible region.
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Sulfonamides with hydroxyphenyl moiety: Synthesis, structure, physicochemical properties, and ability to form complexes with Rh(III) ion
PublicationSulfonamides are the first successfully synthesized antimicrobial drugs. The mechanism of sulfonamides’ antimicrobial action involves competitive inhibition of folic acid synthesis and prevention of the growth and reproduction of bacteria. Even though they have been applied in therapy for more than 75 years, sulfonamides are still the drugs of choice for the treatment of various diseases. The aim of this work was to synthesize...
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Complexes of heteroscorpionate trispyrazolylborate ligands. Part XIII: Molybdenum complexes of hydrobis(5-methyl-3-phenylpyrazolyl)(3-methyl-5-phenylpyrazolyl)borate, hydrotris(3-(2-thienyl)-5-methylpyrazolyl)borate and tetranuclear molybdenum(V) complex of hydrotris(3,5-dimethylpyrazolyl)borate
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The X-ray crystallographic structures, spectral and magnetic properties of nickel(II), copper(II) and cobalt(II) complexes with tetra(3-iso-propylpyrazol-1-yl)borate
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Zinc tri-tert-butoxysilanethiolates. Syntheses, properties and crystal and molecular structures of [Zn{μ-SSi(OBut)3}(acac)]2 and [{(ButO)3SiS}(H2O)2Zn{μ-SSi(OBut)3}Zn(acac){SSi(OBut)3}]
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Copper(II) complexes with substituted imidazole and chlorido ligands: X-ray, UV–Vis, magnetic and EPR studies and chemotherapeutic potential
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Mixed-ligand complexes of zinc(II), cobalt(II) and cadmium(II) with sulfur, nitrogen and oxygen ligands. Analysis of the solid state structure and solution behavior. Implications for metal ion substitution in alcohol dehydrogenase
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The Suzuki cross-coupling reaction for the synthesis of porphyrazine possessing bulky 2,5-(biphenyl-4-yl)pyrrol-1-yl substituents in the periphery
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Photochemical and spectral characterization of peripherally modified porphyrazines
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Porphyrazine with bulky 2-(1-adamantyl)-5-phenylpyrrol-1-yl periphery tuning its spectral and electrochemical properties
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Synthesis and photochemical characteristics of novel tribenzoporphyrazines possessing peripherally annulated tetrahydrodiazepine and diazepine rings
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