Using this result, we can obtain the Euler characteristic of a surface with any number of holes by successively inserting the holes one at a time. For example, since a closed disc has Euler characteristic 1, it follows that a closed disc with 1 hole has Euler characteristic 0, a disc with 2 holes has Euler characteristic −1, and so on.

There are several symbols for powers and roots: for instance, 2⁴ means ‘2 to the power 4’. An alternative to 2⁴ is 24, where the symbol 4, where the symbol

Activity 5: Who enforces the law?

0 hours 10 minutes

Activity 5: Who enforces the law?

0 hours 10 minutes

The importance of science

Science stimulates and excites pupils’ curiosity about phenomena and events in the world around them. It also satisfies this curiosity with knowledge. Because science links direct practical experience with ideas, it can engage learners at many levels. Scientific meth]]> The following statement is from the science National Curriculum in England published in 2000.

The importance of science

Science stimulates and excites pupils’ curiosity about phenomena and events in the world around them. It also satisfies this curiosity with knowledge. Because science links direct practical experience with ideas, it can engage learners at many levels. Scientific meth]]> Time: 100 s to 1000 s

Temperature: 10⁹ K to 3 × 10⁸ K

Energy: 300 keV to 100 keV

As the temperature continued to decrease, protons and neutrons were able to combine to make light nuclei. This marked the beginning of the period referred to as the era of primordial nucleosynthesis (which literally means ‘making nuclei’). The first such reaction to become energetically favoured was that of a single proton and neutron comb]]> Time: 100 s to 1000 s

Temperature: 10⁹ K to 3 × 10⁸ K

Energy: 300 keV to 100 keV

As the temperature continued to decrease, protons and neutrons were able to combine to make light nuclei. This marked the beginning of the period referred to as the era of primordial nucleosynthesis (which literally means ‘making nuclei’). The first such reaction to become energetically favoured was that of a single proton and neutron comb]]> It will probably come as no surprise to you that chemical reactions, including the conversion of arachidonic acid into prostaglandin, do not occur instantaneously and the rate at which they take place can be very variable. Some reactions are over in a flash, such as the burning of gunpowder, and others take months, such as rust formation on a car. All chemical reactions can be speeded up by increasing the temperature of the reactants. In the laboratory one often ‘cooks’ reaction mixtures ]]> It will probably come as no surprise to you that chemical reactions, including the conversion of arachidonic acid into prostaglandin, do not occur instantaneously and the rate at which they take place can be very variable. Some reactions are over in a flash, such as the burning of gunpowder, and others take months, such as rust formation on a car. All chemical reactions can be speeded up by increasing the temperature of the reactants. In the laboratory one often ‘cooks’ reaction mixtures ]]> After studying this Unit you should know:

• that certain minerals are required in the body and that some minerals form essential structural components of tissues;

• that sodium, potassium, calcium and chloride ions are important in maintaining the correct composition of cells and of the tissue fluids around them (homeostasis);

• that some minerals are essential components of important molecules such as hormones and enzymes;

• that the correct]]> After studying this Unit you should know:

  • that certain minerals are required in the body and that some minerals form essential structural components of tissues;

  • that sodium, potassium, calcium and chloride ions are important in maintaining the correct composition of cells and of the tissue fluids around them (homeostasis);

  • that some minerals are essential components of important molecules such as hormones and enzymes;

  • that the correct]]> In preceding sections we examined two ways in which the auditory system may code frequency information: the place theory and phase locking. In this section we will look at the psychophysical evidence for place coding on the basilar membrane by examining the ability of the auditory system to resolve the components of sinusoidal waves in a complex sound – a phenomenon known as frequency selectivity.

    The perception of a sound depends not only on its own frequency and intensity but also o]]> In preceding sections we examined two ways in which the auditory system may code frequency information: the place theory and phase locking. In this section we will look at the psychophysical evidence for place coding on the basilar membrane by examining the ability of the auditory system to resolve the components of sinusoidal waves in a complex sound – a phenomenon known as frequency selectivity.

    The perception of a sound depends not only on its own frequency and intensity but also o]]> For precise localisation of a sound source, binaural cues are required.

    Two types of binaural cue are used to localise non-continuous sounds in the horizontal plane: interaural time differences, which are most efficient for low-frequency sounds (20–1500 Hz) and interaural intensity cues, which are important for high-frequency sounds (1500–20 000 Hz). The frequency responses in the superior olive reflect these differences. The medial superior olive includes neurons that are responsiv]]> For precise localisation of a sound source, binaural cues are required.

    Two types of binaural cue are used to localise non-continuous sounds in the horizontal plane: interaural time differences, which are most efficient for low-frequency sounds (20–1500 Hz) and interaural intensity cues, which are important for high-frequency sounds (1500–20 000 Hz). The frequency responses in the superior olive reflect these differences. The medial superior olive includes neurons that are responsiv]]> Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

    Grateful acknowledgement is made to the following sources for permission:

    Illustrat]]> Except for third party materials and otherwise stated (see terms and conditions), this content is made available under a Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence

    Grateful acknowledgement is made to the following sources for permission:

    Illustrat]]> As we have said, the photons in the 3 K background have been practically free from interaction with anything since about 4 × 10⁵ years after the instant of the big bang. The present angular distribution of the microwave radiation – the way in which it is spread across the sky – is therefore almost the same as it was then. The spectrum we find today depends on the temperatures at that time – for the intensity of the radiation in a particular region of the early Unive]]> As we have said, the photons in the 3 K background have been practically free from interaction with anything since about 4 × 10⁵ years after the instant of the big bang. The present angular distribution of the microwave radiation – the way in which it is spread across the sky – is therefore almost the same as it was then. The spectrum we find today depends on the temperatures at that time – for the intensity of the radiation in a particular region of the early Unive]]> Constants

    Constants

    Constant	Symbol	cgs value	SI value
    Mass of the Sun	M Constants Constant Symbol cgs value SI value Mass of the Sun M iSpot website, where you can share your observations of wildlife, whether these are descriptions or photographs. iSpot is a social networking site that was created to encourage people to engage with nature. It is designed in a way that allows ‘beginners’ to connect with a supportive community of experts and others. ]]> This unit provides access to the iSpot website, where you can share your observations of wildlife, whether these are descriptions or photographs. iSpot is a social networking site that was created to encourage people to engage with nature. It is designed in a way that allows ‘beginners’ to connect with a supportive community of experts and others. ]]> Even the simplest organisms can detect and respond to events in their ever-changing environment. Similarly, within a multicellular organism, cells are surrounded by an extracellular environment from which signals are received and responded to. Extracellular events are decoded and transmitted to relevant parts of individual cells by way of a series of activation/deactivation steps involving many intracellular molecules. This relay of information along molecular pathways is called signal tra]]> Even the simplest organisms can detect and respond to events in their ever-changing environment. Similarly, within a multicellular organism, cells are surrounded by an extracellular environment from which signals are received and responded to. Extracellular events are decoded and transmitted to relevant parts of individual cells by way of a series of activation/deactivation steps involving many intracellular molecules. This relay of information along molecular pathways is called signal tra]]> Compared with other cytoskeletal elements, intermediate filaments are more like a fixed scaffolding for the cell. They have a higher tensile strength than microtubules and microfilaments. Consequently they contribute greatly to the overall integrity of the cell and preservation of its shape. Not all eukaryotic cells have cytoskeletal intermediate filaments, and of those that do, each cell type has its own distinct set of intermediate filaments. The intermediate filaments, being cell-type spec]]> Compared with other cytoskeletal elements, intermediate filaments are more like a fixed scaffolding for the cell. They have a higher tensile strength than microtubules and microfilaments. Consequently they contribute greatly to the overall integrity of the cell and preservation of its shape. Not all eukaryotic cells have cytoskeletal intermediate filaments, and of those that do, each cell type has its own distinct set of intermediate filaments. The intermediate filaments, being cell-type spec]]> Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit: The content acknowledged below is Proprietary and used under licence (not subject to Creative Commons licence). See Terms and Conditions. Figures Figure 1 Copyr]]> Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit: The content acknowledged below is Proprietary and used under licence (not subject to Creative Commons licence). See Terms and Conditions. Figures Figure 1 Copyr]]> An object that fluctuates in brightness on a timescale Δt can have a radius no greater than R ∼ cΔt. The point-like nature of AGNs and their rapid variability imply that the emitting region is smaller than the size of the Solar System. The central engine of a typical AGN is believed to contain a supermassive black hole of mass ∼108M ⊙ and Schwarzschild radius ]]> An object that fluctuates in brightness on a timescale Δt can have a radius no greater than R ∼ cΔt. The point-like nature of AGNs and their rapid variability imply that the emitting region is smaller than the size of the Solar System. The central engine of a typical AGN is believed to contain a supermassive black hole of mass ∼108M ⊙ and Schwarzschild radius ]]> Please donate today for 2013. From Ron Paul Let me tell you, the work of the Mises Institute is crucial. This is important. This is more important than all political action. We have to change people’s hearts and minds, and their under]]> Please donate today for 2013. From Ron Paul Let me tell you, the work of the Mises Institute is crucial. This is important. This is more important than all political action. We have to change people’s hearts and minds, and their under]]>