Quotient inductive-inductive types (QIITs) generalise inductive types in two ways: a QIIT can have more than one sort and the later sorts can be indexed over the previous ones. In addition, equality constructors are also allowed. We work in a setting with uniqueness of identity proofs, hence we use the term QIIT instead of higher inductive-inductive type. An example of a QIIT is the well-typed (intrinsic) syntax of type theory quotiented by conversion. In this paper first we specify finitary QIITs using a domain-specific type theory which we call the theory of signatures. The syntax of the theory of signatures is given by a QIIT as well. Then, using this syntax we show that all specified QIITs exist and they have a dependent elimination principle. We also show that algebras of a signature form a category with families (CwF) and use the internal language of this CwF to show that dependent elimination is equivalent to initiality.

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Shading effect of external nets of different colours (white, green, yellow and red) on the yield of two “kapija” pepper (Capsicum anuum L.) cultivars was examined in walk-in plastic tunnels in Hungary under real cultivation circumstances. Shading nets decreased incoming radiation by 23-39% and reduced photosynthetically active radiation by 32-46%. The highest retention was obtained by yellow and green nets, in the range of 450-550 nm and 550-670 nm, respectively. Relation was reported between the degree of shading and the average air temperature of the tunnels, however, treatments did not decrease tunnel air temperature significantly, compared to that of unshaded and paint-shaded control tunnels. This can be explained by the applied proper ventilation and mist irrigation. A strong and negative relation was noted between the intensity of shading and the relative chlorophyll content (SPAD value) of leaves. Shading net treatments did not increase yields, yellow and green nets even decreased it. Instead of tunnel air temperature, yield was mainly affected by photosynthetically active radiation in the experiment. Strong positive linear relation was declared between the chlorophyll content of the leaves and the yield. Results of the current research led to the conclusions that under Hungarian climatic conditions the use of shading nets was less justified if proper cooling techniques (ventilation and mist irrigation) were applied; even under the relatively high incident radiation experienced during the trials. In greenhouses of less favourable climatic conditions, red or white shading nets are recommended instead of commonly used green ones in Hungary.

Shading effect of external nets of different colours (white, green, yellow and red) on the yield of two "kapija" pepper (Capsicum anuum L.) cultivars was examined in walk-in plastic tunnels in Hungary under real cultivation circumstances. Shading nets decreased incoming radiation by 23-39% and reduced photosynthetically active radiation by 32-46%. The highest retention was obtained by yellow and green nets, in the range of 450-550 nm and 550-670 nm, respectively. Relation was reported between the degree of shading and the average air temperature of the tunnels, however, treatments did not decrease tunnel air temperature significantly, compared to that of unshaded and paint-shaded control tunnels. This can be explained by the applied proper ventilation and mist irrigation. A strong and negative relation was noted between the intensity of shading and the relative chlorophyll content (SPAD value) of leaves. Shading net treatments did not increase yields, yellow and green nets even decreased it. Instead of tunnel air temperature, yield was mainly affected by photosynthetically active radiation in the experiment. Strong positive linear relation was declared between the chlorophyll content of the leaves and the yield. Results of the current research led to the conclusions that under Hungarian climatic conditions the use of shading nets was less justified if proper cooling techniques (ventilation and mist irrigation) were applied; even under the relatively high incident radiation experienced during the trials. In greenhouses of less favourable climatic conditions, red or white shading nets are recommended instead of commonly used green ones in Hungary.

Quotient inductive-inductive types (QIITs) are generalized inductive types which allow sorts to be indexed over previously declared sorts, and allow usage of equality constructors. QIITs are especially useful for algebraic descriptions of type theories and constructive definitions of real, ordinal and surreal numbers. We develop new metatheory for large QI-ITs, large elimination, recursive equations and infinitary constructors. As in prior work, we describe QIITs using a type theory where each context represents a QIIT signature. However, in our case the theory of signatures can also describe its own signature, modulo universe sizes. We bootstrap the model theory of signatures using self-description and a Church-coded notion of signature, without using complicated raw syntax or assuming an existing internal QIIT of signatures. We give semantics to described QI-ITs by modeling each signature as a finitely complete CwF (category with families) of algebras. Compared to the case of finitary QIITs, we additionally need to show invariance under algebra isomorphisms in the semantics. We do this by modeling signature types as isofibrations. Finally, we show by a term model construction that every QIIT is constructible from the syntax of the theory of signatures.

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Abstract. Title of the paper: Milk yield an milk quality of beef cows during the suckling period The milk yield of suckling cows is an important requirement for the growth of weaning calves. The daily milk yield of 57 suckling cows was recorded in different stages of suckling period. As methods of the milk recording were used "weigh – suckle – weigh" and machine milking with application of oxytocin. The means of the 200 days milk yield were 1,754 kg in suckling cows of the Red Angus breed at Hungarian farm and 2,868 kg for different genotypes on a grassland location in the North of Germany. On average, the percentage of milk fat was x = 4.26 % ± 1.17 %, of protein x = 3.62 % ± 0.39 % and of lactose x = 4.80 % + 0.35 %, respectively. Significant relations were recorded between the milk yield in the first 6th months of suckling period and the daily weight gain (coefficients from r = 0.541 to r = 0.581).

There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and normalisation. One option is to embed the syntax deeply, by using inductive definitions in a proof assistant. However, in this case the handling of definitional equalities becomes technically challenging. Alternatively, we can reuse conversion checking in the metatheory by shallowly embedding the object theory. In this paper, we consider the standard model of a type theoretic object theory in Agda. This model has the property that all of its equalities hold definitionally, and we can use it as a shallow embedding by building expressions from the components of this model. However, if we are to reason soundly about the syntax with this setup, we must ensure that distinguishable syntactic constructs do not become provably equal when shallowly embedded. First, we prove that shallow embedding is injective up to definitional equality, by modelling the embedding as a syntactic translation targeting the metatheory. Second, we use an implementation hiding trick to disallow illegal propositional equality proofs and constructions which do not come from the syntax. We showcase our technique with very short formalisations of canonicity and parametricity for Martin-Löf type theory. Our technique only requires features which are available in all major proof assistants based on dependent type theory.