Systematic screening of bryophytes for antitumor agents

References are made to cytotoxic and/or antitumor compounds that have been isolated - ansamitocin P-3 from Claopodium crispifolium (Hook.) Ren. & Card. and Anomodon attenuatus Hueb., or an associated actinomycete, and ohioensins and pallidisetums from Polytrichum spp. Several hundred collections, which have been obtained from temperate regions of North America during 1990 and 1991, are currently being screened in new bioassays; active sesquiterpene lactones have been recently isolated from species of Porella. The methodologies of collecting and screening bryophyte samples are discussed with consideration to costs based on expected number of samples that might be collected in a day, the diversity in the collections as related to phytogeography and vegetation types, and the bryophyte cover that is vanishing in many forest regions of the United States. The difficulties in obtaining large collections for isolation of active agents are also discussed by examplerecollection of Claopodium crispifolium

The fruticose genera in the Ramalinaceae (Ascomycota, Lecanoromycetes): their diversity and evolutionary history

peer reviewedWe present phylogenetic analyses of the fruticose Ramalinaceae based on extensive collections from many parts of the world, with a special focus on the Vizcaíno deserts in northwestern Mexico and the coastal desert in Namibia. We generate a four-locus DNA sequence dataset for accessions of Ramalina and two additional loci for Niebla and Vermilacinia. Four genera are strongly supported: the subcosmopolitan Ramalina, the new genus Namibialina endemic to SW Africa, and a duo formed by Niebla and Vermilacinia, endemic to the New World except the sorediate V. zebrina that disjunctly occurs in Namibia. The latter three genera are restricted to coastal desert and chaparral where vegetation depends on moisture from ocean fog. Ramalina is subcosmopolitan and much more diverse in its ecology. We show that Ramalina and its sister genus Namibialina diverged from each other at c. 48 Myrs, whereas Vermilacinia and Niebla split at c. 30 Myrs. The phylogeny of the fruticose genera remains unresolved to their ancestral crustose genera. Species delimitation within Namibialina and Ramalina is rather straightforward. The phylogeny and taxonomy of Vermilacinia are fully resolved, except for the two youngest clades of corticolous taxa, and support current taxonomy, including four new taxa described here. Secondary metabolite variation in Niebla generally coincides with major clades which are comprised of species complexes with still unresolved phylogenetic relationships. A micro-endemism pattern of allopatric species is strongly suspected for both genera, except for the corticolous taxa within Vermilacinia. Both Niebla and saxicolous Vermilacinia have chemotypes unique to species clades that are largely endemic to the Vizcaíno deserts. The following new taxa are described: Namibialina gen. nov. with N. melanothrix (comb. nov.) as type species, a single new species of Ramalina (R. krogiae) and four new species of Vermilacinia (V. breviloba, V. lacunosa, V. pustulata and V. reticulata). The new combination V. granulans is introduced. Two epithets are reintroduced for European Ramalina species: R. crispans (= R. peruviana auct. eur.) and R. rosacea (= R. bourgeana auct. p.p). A lectotype is designated for Vermilacinia procera. A key to saxicolous species of Vermilacinia is presented

Roots and Critical Points of Complex Polynomials: Applications of Algorithms in Real Algebra, Moment Theory, Convex Analysis, Optimization, and Positive Polynomials to a Conjecture in Pure Mathematics

Conjecture 0.1 (Conjecture of Blagovest Sendov (1958))For a complex polynomial of degree two or more with all its roots contained within the closed unit disk, each root has a critical point within unit distance.We introduce a countable collection of conjectures – one for each degree – by transferring into languages of Real Algebra. For fixed degree, each conjecture is decidable. Thus, we consider decidable statements in Real Algebra. For each of these decidable statements, we seek for certificates. We provide variations of this theme for different contexts: Positivstellensatz, Nichtnegativstellensatz and real radical ideal membership. In our context, our positivity certificates (or membership certificates) provide proof when achieved. We also find plenty of novel numerical evidence substantiating our conjectures.Keywords: Math, Maths, Mathematic, Mathematics, Mathematical, Pure Mathematics, Theoretical Mathematics, Applied Mathematics, Algorithm, Algorithms, Roots, Critical Points, Complex Analysis, Complex Polynomials, Real Algebra, Real Polynomials, Real Closed Field, Real Radical Ideal, Real Radical Ideal Membership, Ideal, Ideal Membership, Groebner, Gr ̈obner, Groebner Fan, Gr ̈obner Fan, Certificate, Certificate of Real Radical Ideal Membership, Certificate of Ideal Membership, Buchberger’s algorithm, S-Procedure, Real Algebraic Geometry, Algebraic Geometry, Linear Matrix Inequality, Linear Matrix Inequalities, LMI, Cylindrical Algebraic Decomposition, Procedure, Resultant, Lifting, Elimination, Input, Output, Semidefinite, Semidefinite Set, Semidefinite Sets, Semidefinite Programming, Nonlinear Programming, SDP, Relaxation Order, Semidefinite Relaxation, Slack Variable, Linear Operator, Linear Algebra, Moment, Moments, Moment Theory, Optimization, Optimum, Maximum, Supremum, Infimum, Minimum, Optimal, Maximal, Minimal, Extremal Polynomials, Convex Optimization, Convex Analysis, Functional Analysis, Function, Functional, Measure, Positivity, Positivity Certificate, Certificate, Polynomial, Positive Polynomial, Positive Polynomials, Sums of Squares, Ring, Preordering, Quadratic Module, Anneaux preordonnes, Rational Sums of Squares, SOS, Hilbert, David Hilbert, Artin, Emil Artin, Nullstellensatz, Positivestellensatz, Nichtnegativstellensatz, Nonnegative, Non-negative, Nonnegative Polynomial, Nonnegative Polynomials, Non-negative Polynomials, Tarski, Transfer Principle, Tarski-Transfer, Tarski-Seidenberg, Tarski-Seidenberg Principle, Dynamics, Nonlinear Dynamics, Fundamental Theorem of Algebra, Cauchy Integral Formula, The Argument Principle, Liouville’s Theorem, Rouche’s Theorem, Asymptotic, Asymptotics, Derivative, Differential Operator, Pullback, Complexity, Double Exponential, Computational Complexity, Numerics, Numerical, Decision, Decision Theory, Decision Problem, Decision Problems, Decidable, Axiom, Axiomatic, Independence, Model Theory, Higher-Order Logic, Conjecture, Blagovest Sendov, Sendov’s Conjecture, Ilief’s Conjecture, Duality, Duality Gap, Moment and Positive Polynomial Duality, Machine Error, Machine Precision, Validation, True, Truth, Incomplete, Incompleteness, Complete, Completeness, Contrapositive, Consistent, Formal Language, Language, Bounds, Global Optimum, Global Optimization, Constrained Optimizatio

Roots and Critical Points of Complex Polynomials: Applications of Algorithms in Real Algebra, Moment Theory, Convex Analysis, Optimization, and Positive Polynomials to a Conjecture in Pure Mathematics

Conjecture 0.1 (Conjecture of Blagovest Sendov (1958))For a complex polynomial of degree two or more with all its roots contained within the closed unit disk, each root has a critical point within unit distance.We introduce a countable collection of conjectures – one for each degree – by transferring into languages of Real Algebra. For fixed degree, each conjecture is decidable. Thus, we consider decidable statements in Real Algebra. For each of these decidable statements, we seek for certificates. We provide variations of this theme for different contexts: Positivstellensatz, Nichtnegativstellensatz and real radical ideal membership. In our context, our positivity certificates (or membership certificates) provide proof when achieved. We also find plenty of novel numerical evidence substantiating our conjectures.Keywords: Math, Maths, Mathematic, Mathematics, Mathematical, Pure Mathematics, Theoretical Mathematics, Applied Mathematics, Algorithm, Algorithms, Roots, Critical Points, Complex Analysis, Complex Polynomials, Real Algebra, Real Polynomials, Real Closed Field, Real Radical Ideal, Real Radical Ideal Membership, Ideal, Ideal Membership, Groebner, Gr ̈obner, Groebner Fan, Gr ̈obner Fan, Certificate, Certificate of Real Radical Ideal Membership, Certificate of Ideal Membership, Buchberger’s algorithm, S-Procedure, Real Algebraic Geometry, Algebraic Geometry, Linear Matrix Inequality, Linear Matrix Inequalities, LMI, Cylindrical Algebraic Decomposition, Procedure, Resultant, Lifting, Elimination, Input, Output, Semidefinite, Semidefinite Set, Semidefinite Sets, Semidefinite Programming, Nonlinear Programming, SDP, Relaxation Order, Semidefinite Relaxation, Slack Variable, Linear Operator, Linear Algebra, Moment, Moments, Moment Theory, Optimization, Optimum, Maximum, Supremum, Infimum, Minimum, Optimal, Maximal, Minimal, Extremal Polynomials, Convex Optimization, Convex Analysis, Functional Analysis, Function, Functional, Measure, Positivity, Positivity Certificate, Certificate, Polynomial, Positive Polynomial, Positive Polynomials, Sums of Squares, Ring, Preordering, Quadratic Module, Anneaux preordonnes, Rational Sums of Squares, SOS, Hilbert, David Hilbert, Artin, Emil Artin, Nullstellensatz, Positivestellensatz, Nichtnegativstellensatz, Nonnegative, Non-negative, Nonnegative Polynomial, Nonnegative Polynomials, Non-negative Polynomials, Tarski, Transfer Principle, Tarski-Transfer, Tarski-Seidenberg, Tarski-Seidenberg Principle, Dynamics, Nonlinear Dynamics, Fundamental Theorem of Algebra, Cauchy Integral Formula, The Argument Principle, Liouville’s Theorem, Rouche’s Theorem, Asymptotic, Asymptotics, Derivative, Differential Operator, Pullback, Complexity, Double Exponential, Computational Complexity, Numerics, Numerical, Decision, Decision Theory, Decision Problem, Decision Problems, Decidable, Axiom, Axiomatic, Independence, Model Theory, Higher-Order Logic, Conjecture, Blagovest Sendov, Sendov’s Conjecture, Ilief’s Conjecture, Duality, Duality Gap, Moment and Positive Polynomial Duality, Machine Error, Machine Precision, Validation, True, Truth, Incomplete, Incompleteness, Complete, Completeness, Contrapositive, Consistent, Formal Language, Language, Bounds, Global Optimum, Global Optimization, Constrained Optimizatio

Roots and Critical Points of Complex Polynomials: Applications of Algorithms in Real Algebra, Moment Theory, Convex Analysis, Optimization, and Positive Polynomials to a Conjecture in Pure Mathematics

Conjecture 0.1 (Conjecture of Blagovest Sendov (1958)): For a complex polynomial of degree two or more with all its roots contained within the closed unit disk, each root has a critical point within unit distance. We introduce a countable collection of conjectures – one for each degree – by transferring into languages of Real Algebra. For fixed degree, each conjecture is decidable. Thus, we consider decidable statements in Real Algebra. For each of these decidable statements, we seek for certificates. We provide variations of this theme for different contexts: Positivstellensatz, Nichtnegativstellensatz and real radical ideal membership. In our context, our positivity certificates (or membership certificates) provide proof when achieved. We also find plenty of novel numerical evidence substantiating our conjectures

RELATIONSHIPS BETWEEN PLANT FOLKLORE AND ANTITUMOR ACTIVITY: AN HISTORICAL REVIEW

Volume: 21Start Page: 2205End Page: 224

A PHYTOGEOGRAPHICAL ANALYSIS OF TAXUS (TAXACEAE) BASED ON LEAF ANATOMICAL CHARACTERS

Volume: 1Start Page: 291End Page: 33

TAXONOMY AND NOMENCLATURE OF TAXUS (TAXACEAE)

Volume: 1Start Page: 203End Page: 28

Corrigendum: Spjut R, Simon A, Guissard M, Magain N, Sérusiaux E (2020) The fruticose genera in the Ramalinaceae (Ascomycota, Lecanoromycetes): their diversity and evolutionary history. MycoKeys 73: 1–68. https://doi.org/10.3897/mycokeys.73.47287

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