Rigidity of holomorphic maps between fiber spaces

In the study of holomorphic maps, the term "rigidity" refers to certain types of results that give us very specific information about a general class of holomorphic maps owing to the geometry of their domains or target spaces. Under this theme, we begin by studying when, given two compact connected complex manifolds $X$ and $Y$, a degree-one holomorphic map $f: Y\to X$ is a biholomorphism. Given that the real manifolds underlying $X$ and $Y$ are diffeomorphic, we provide a condition under which $f$ is a biholomorphism. Using this result, we deduce a rigidity result for holomorphic self-maps of the total space of a holomorphic fiber space. Lastly, we consider products $X=X_1\times X_2$ and $Y=Y_1\times Y_2$ of compact connected complex manifolds. When $X_1$ is a Riemann surface of genus $\geq 2$, we show that any non-constant holomorphic map $F:Y\to X$ is of a special form.Comment: 7 pages; expanded Remark 1.2; provided an explanation for the notation in Section 3; to appear in Internat. J. Mat

The Fujiki class and positive degree maps

We show that a map between complex-analytic manifolds, at least one of which is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of "domination" introduced by Gromov is in fact a partial order.Comment: 6 pages; significantly restructured first & last sections; corrected statement of Result 3.4 (formerly Result 4.4); added references; to appear in Complex Manifold

Return on environment: An objective indicator to validate life cycle assessments?

The Return on Environment (ROE) is developed, and tested, as an objective indicator to support the results of Life Cycle Assessments. It is based on the observation that a ratio of life cycle costs incurred throughout the extraction, transport, manufacturing, use and disposal stages, to the selling price, appears to scale linearly with a quantitative impact assessment. ROE is therefore a normalization method which permits comparison of new assessments with existing data, even from products with quite different characteristics. It can, alternatively, be applied to estimate either the life cycle cost, or quantify environmental impact, provided the other is known. Like its economic cousin, the return on investment, cases studied typically have ROEs in over the range of 2-20%. ROE is intended as a preliminary estimation method, akin to engineering costing, which has a precision of +-30%. As such, it can be used to rapidly determine if a more detailed cost assessment can be justified and, if so, where the efforts should be oriented. ROE is a measurable life cycle index intended to render LCAs more suitable for decision making. A further benefit that ROE provides is the guidance to a life cycle practitioner, or product development team, to assess if sufficient data has been collected, or if costs and impacts have been over or under-estimated. It has advantages over specific ecoindicators, such as manufacturing energy or waste emissions, which are both product specific and subjective. The Return on Environment also serves as a systematic index for reporting improvements or as a relative environmental ratin

Proučavanje četvrte generacije kvarkova i neutralnih struja koje mijenjaju okus

The decay of the fourth-generation down-type quark b\u27 → bγ and b\u27 → bg has been studied as an extension of the standard model using evolution of the mass-based fourth generation CKM matrix with CP violation phase equal to zero. Range of the masses of fourth generation down-type quark b\u27 and up-type quark t\u27 have been taken with due observance of the constraint imposed by the present experimental value of the ρ parameter, keeping in view the mass difference of the fourth generation quark doublet. The decay width of b\u27 → bγ also has been studied, however, with correction up to the leading QCD logarithms for six active flavours after the W boson, t and t\u27 quarks have been integrated out using operator product expansion. Strong interaction coupling constant is taken on matching scale of Z boson mass.Razmatraju se raspadi četvrte generacije kvarkova tipa ”dolje” b\u27 → bγ i b\u27 → bg kao proširenje standardnog modela, primjenom evolucije CKM matrice četvrte generacije zasnovane na masi, s fazom kršenja CP simetrije jednakom nula. Izabrali smo područje masa kvarkova četvrte generacije tipa ”dolje” b\u27 i tipa ”gore” t\u27 gledajući ograničenje koje postavlja sadašnja eksperimentalna vrijednost parametra ρ, drzeći u vidu razliku masa kvarkovskog dubleta četvrte generacije. Također se proučava širina raspada b\u27 → bγ, ali s popravkom do vodećih QCD logaritama za šest aktivnih okusa, nakon sto su W bozon, te t i t\u27 kvarkovi izintegrirani primjenom razvoja operatorskog umnoška. Konstanta jake interakcije uzela se je u skladu s masom Z bozona

Ograničenje trilinearnoga baždarnog vezanja raspadom b → sγ uzevši u obzir mogućnost četvrte generacije kvarkova

We examine the indirect effect of the new physics. The virtual effects of the trilinear gauge coupling of the photon to W+W- on the b → sγ decay has been tested considering the possibility of the fourth generation in the quark sector, with corrections up to leading QCD logarithmas, using evolution of the fourth-generation CKM matrix with CP-violation phase equal to zero. Range of mass of the fourth-generation down-type quark b˘ and that of fourth generation up-type quark t˘ have been taken with due observance of the constraint imposed by the present experimental value of the ρ parameter, keeping in view the mass difference of the fourth-generation quark doublet. Strong-interaction coupling constant, however, is taken on matching scale of Z-boson mass.Virtualni učinci trilinearnoga baždarnog vezanja fotona na W+¬ W- na raspad b → sγ se provjeravaju uz pretpostavku moguće četvrte generacije kvarkova, s popravkama do vodećih QCD logaritama, primjenom razvoja CKM matrice četvrte generacije i fazom kršenja CP-invarijantnosti jednakom nula. Uzeta su u obzir ograničenja izmjerenom vrijednošću parametra ρ